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WiLE.m
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WiLE.m
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(* ::Package:: *)
If[MemberQ[$Packages,"WiLE`"],Print["The package WiLE is already loaded!"];Abort[]]
BeginPackage["WiLE`"]
Print["-*-*-*-*-WiLE-1.0-*-*-*-*-\n
Wilson Loop Expansion\n
Author: Michelangelo Preti, DESY Hamburg\n
-*-*-*-*-*-*-*-*-*-*-*-*-*-\n
WiLE loaded! The new provided commands are:\n
- WiLE\n
- WiLEFullorder\n
- WiLESimplify"]
WiLE::usage="Print the WiLE input window. Run the command without any argument."
WiLESimplify::usage="WiLESimplify[x]
Simplify the WiLE and WiLEFullorder outputs x. "
WiLEFullorder::usage="Print the WiLEFullorder input window. Run the command without any argument."
Begin["`Private`"]
(* ::Section::Closed:: *)
(*Notation*)
Notation`AutoLoadNotationPalette = False
Needs["Notation`"]
(*Initialize the notation*)
(*Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox[SubscriptBox["A", "a_"], "\[Mu]_"], ")"}], "i_"], "j_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"A", "[", RowBox[{RowBox[{"\[Tau]", "[", "a_", "]"}], ",", "\[Mu]_", ",", "i_", ",", "j_"}], "]"}]]]
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Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox[SubscriptBox[OverscriptBox["A", "^"], SubscriptBox["z", "a_"]], "\[Mu]_"], ")"}], OverscriptBox["i_", "^"]], OverscriptBox["j_", "^"]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Ah", "[", RowBox[{RowBox[{"z", "[", "a_", "]"}], ",", "\[Mu]_", ",", RowBox[{"h", "[", "i_", "]"}], ",", RowBox[{"h", "[", "j_", "]"}]}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox[SubscriptBox[SubscriptBox["\[Psi]", "a_"], "J_"], "\[Alpha]_"], ")"}], OverscriptBox["i_", "^"]], "j_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"\[Psi]", "[", RowBox[{RowBox[{"\[Tau]", "[", "a_", "]"}], ",", "\[Alpha]_", ",", "J_", ",", RowBox[{"h", "[", "i_", "]"}], ",", "j_"}], "]"}]]]
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Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SubscriptBox[SubscriptBox["C", "a_"], "J_"], ")"}], "i_"], OverscriptBox["j_", "^"]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"C", "[", RowBox[{RowBox[{"\[Tau]", "[", "a_", "]"}], ",", "J_", ",", "i_", ",", RowBox[{"h", "[", "j_", "]"}]}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox[SubscriptBox["Cb", "a_"], "J_"], ")"}], OverscriptBox["i_", "^"]], "j_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Cb", "[", RowBox[{RowBox[{"\[Tau]", "[", "a_", "]"}], ",", "J_", ",", RowBox[{"h", "[", "i_", "]"}], ",", "j_"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SubscriptBox[SubscriptBox["C", SubscriptBox["z", "a_"]], "J_"], ")"}], "i_"], OverscriptBox["j_", "^"]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"C", "[", RowBox[{RowBox[{"z", "[", "a_", "]"}], ",", "J_", ",", "i_", ",", RowBox[{"h", "[", "j_", "]"}]}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox[SubscriptBox["Cb", SubscriptBox["z", "a_"]], "J_"], ")"}], OverscriptBox["i_", "^"]], "j_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Cb", "[", RowBox[{RowBox[{"z", "[", "a_", "]"}], ",", "J_", ",", RowBox[{"h", "[", "i_", "]"}], ",", "j_"}], "]"}]]]*)
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[SubscriptBox["M", "a_"], "J1_"], "J2_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`M", "[", RowBox[{RowBox[{"Global`\[Tau]", "[", "a_", "]"}], ",", "J1_", ",", "J2_"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[SubscriptBox[OverscriptBox["M", "^"], "a_"], "J1_"], "J2_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`Mh", "[", RowBox[{RowBox[{"Global`\[Tau]", "[", "a_", "]"}], ",", "J1_", ",", "J2_"}], "]"}]]]
(*Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SubscriptBox[SubscriptBox["\[CapitalPsi]", SubscriptBox["z", "a_"]], RowBox[{" ", RowBox[{"\[Alpha]_", " ", "J_"}]}]], ")"}], OverscriptBox["i_", "^"]], "j_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"\[CapitalPsi]", "[", RowBox[{RowBox[{"z", "[", "a_", "]"}], ",", "\[Alpha]_", ",", "J_", ",", RowBox[{"h", "[", "i_", "]"}], ",", "j_"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox[SubscriptBox["\[CapitalPsi]b", SubscriptBox["z", "a_"]], RowBox[{"\[Alpha]_", " ", "J_"}]], ")"}], "i_"], OverscriptBox["j_", "^"]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"\[CapitalPsi]b", "[", RowBox[{RowBox[{"z", "[", "a_", "]"}], ",", "\[Alpha]_", ",", "J_", ",", "i_", ",", RowBox[{"h", "[", "j_", "]"}]}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[RowBox[{"(", SuperscriptBox["\[Gamma]", "\[Mu]_"], ")"}], "\[Alpha]_"], "\[Beta]_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{RowBox[{"\[Gamma]", "[", "du", "]"}], "[", RowBox[{"\[Mu]_", ",", "\[Alpha]_", ",", "\[Beta]_"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[RowBox[{"(", SuperscriptBox["\[Gamma]", "\[Mu]_"], ")"}], RowBox[{"\[Alpha]_", " ", "\[Beta]_"}]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{RowBox[{"\[Gamma]", "[", "uu", "]"}], "[", RowBox[{"\[Mu]_", ",", "\[Alpha]_", ",", "\[Beta]_"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox[SuperscriptBox[RowBox[{"(", SuperscriptBox["\[Gamma]", "\[Mu]_"], ")"}], "\[Alpha]_"], "\[Beta]_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{RowBox[{"\[Gamma]", "[", "ud", "]"}], "[", RowBox[{"\[Mu]_", ",", "\[Alpha]_", ",", "\[Beta]_"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox[RowBox[{"(", SuperscriptBox["\[Gamma]", "\[Mu]_"], ")"}], RowBox[{"\[Alpha]_", " ", "\[Beta]_"}]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{RowBox[{"\[Gamma]", "[", "dd", "]"}], "[", RowBox[{"\[Mu]_", ",", "\[Alpha]_", ",", "\[Beta]_"}], "]"}]]]*)
Notation[ParsedBoxWrapper[RowBox[{SubscriptBox["n", RowBox[{"a_", " ", "J_"}]], " "}]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`nJ", "[", RowBox[{RowBox[{"Global`\[Tau]", "[", "a_", "]"}], ",", "J_"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[OverscriptBox["n", "\[Dash]"], "a_"], "J_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`nJb", "[", RowBox[{RowBox[{"Global`\[Tau]", "[", "a_", "]"}], ",", "J_"}], "]"}]]]
(*Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[SubscriptBox["\[Eta]", "a_"], "J_"], "\[Alpha]_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"\[Eta]", "[", RowBox[{RowBox[{"\[Tau]", "[", "a_", "]"}], ",", "\[Alpha]_", ",", "J_"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[SubscriptBox["\[Eta]b", "a_"], "\[Alpha]_"], "J_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"\[Eta]b", "[", RowBox[{RowBox[{"\[Tau]", "[", "a_", "]"}], ",", "\[Alpha]_", ",", "J_"}], "]"}]]]*)
Notation[ParsedBoxWrapper[SubscriptBox["n", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`nJ", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox[OverscriptBox["n", "\[Dash]"], "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`nJb", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox[SubscriptBox[OverscriptBox["x", "."], "a_"], "\[Mu]_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`xp", "[", RowBox[{RowBox[{"Global`\[Tau]", "[", "a_", "]"}], ",", "\[Mu]_"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["x", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`x", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["z", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`z", "[", "a_", "]"}]]]
Notation[ParsedBoxWrapper[SuperscriptBox["\[Gamma]", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Gamma]", "[", "a_", "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["M", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`M", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox[OverscriptBox["M", "^"], "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`Mh", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["\[Eta]", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Eta]", "[", RowBox[{"Global`x", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox[OverscriptBox["\[Eta]", "\[Dash]"], "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Eta]b", "[", RowBox[{"Global`x", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}], "]"}]]]
Notation[ParsedBoxWrapper[RowBox[{SuperscriptBox[SubscriptBox["d", "a_"], "b_"], "[", "c_", "]"}]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`d", "[", RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["\[Epsilon]", RowBox[{"A_", " ", "B_", " ", "C_", " ", "D_"}]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Epsilon]\[Epsilon]", "[", RowBox[{"A_", ",", "B_", ",", "C_", ",", "D_"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["\[Epsilon]", RowBox[{"A_", " ", "B_", " ", "C_", " "}]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Epsilon]", "[", RowBox[{"A_", ",", "B_", ",", "C_"}], "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["\[Mu]", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Mu]", "[", "a_", "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["\[Nu]", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Nu]", "[", "a_", "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["\[Sigma]", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`\[Sigma]", "[", "a_", "]"}]]]
Notation[ParsedBoxWrapper[SubscriptBox["J", "a_"]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`J", "[", "a_", "]"}]]]
Notation[ParsedBoxWrapper[RowBox[{"mod", "[", SubscriptBox[OverscriptBox["x", "."], "a_"], "]"}]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"Global`mod", "[", RowBox[{"Global`xp", "[", RowBox[{"Global`\[Tau]", "[", "a_", "]"}], "]"}], "]"}]]]
SetAttributes[\[Delta]\[Delta],Orderless]
SetAttributes[\[Delta]\[Delta]1,Orderless]
(* ::Section::Closed:: *)
(*Superconnection*)
(* Definition of fermionic superconnection *)
Con[a_,i_,j_]:=Block[{\[Mu]=Unique[\[Mu]],\[Alpha]=Unique[\[Alpha]],J=Unique[J],J1=Unique[J1],J2=Unique[J2],k=Unique[k]},{{ A[\[Tau][a],\[Mu],i,j]xp[\[Tau][a],\[Mu]]-(2\[Pi] I)/Global`\[Kappa] Global`M[Global`\[Tau][a],J1,J2]Global`mod[Global`xp[\[Tau][a]]]C[\[Tau][a],J2,i,h[k]]Cb[\[Tau][a],J1,h[k],j],I Sqrt[(2\[Pi])/Global`\[Kappa]]Global`mod[Global`xp[\[Tau][a]]] \[Eta][\[Tau][a],\[Alpha],J]\[Psi]b[\[Tau][a],\[Alpha],J,i,h[j]]},{-I Sqrt[(2\[Pi])/Global`\[Kappa]]Global`mod[Global`xp[\[Tau][a]]] \[Psi][\[Tau][a],\[Alpha],J,h[i],j]\[Eta]b[\[Tau][a],\[Alpha],J], Ah[\[Tau][a],\[Mu],h[i],h[j]]xp[\[Tau][a],\[Mu]]-(2\[Pi] I)/Global`\[Kappa] Global`Mh[Global`\[Tau][a],J1,J2]Global`mod[Global`xp[\[Tau][a]]]Cb[\[Tau][a],J1,h[i],k]C[\[Tau][a],J2,k,h[j]]}}]
(* Expansion of the upper-left and lower-right blocks *)
Expansionup[s_]:=((-I)^s (Dot@@Table[Con[j,i[j],i[j+1]],{j,1,s}])[[1,1]])/.i[s+1]->i[1]//Expand
Expansiondown[s_]:=(-I)^s (Dot@@Table[Con[j,i[j],i[j+1]],{j,1,s}])[[2,2]]/.i[s+1]->i[1]//Expand
Expansion[s_]:={Expansionup[s],Expansiondown[s]}
(* ::Section::Closed:: *)
(*Vertices*)
(* Vertices defined as a list. The length of the list depend from the number of elements of the vertex for a fixed set of interacting fields.
x=position of the vertex
j=name of the gauge index
\[Alpha]=name of the spin index *)
VertexA\[Psi]\[Psi][x_,j_,\[Alpha]_]:=Block[{\[Mu]=Unique[\[Mu]],J=Unique[J]},{-\[Gamma][du][\[Mu],\[Alpha][1],\[Alpha][2]]\[CenterDot]{\[CapitalPsi]b[z[x],\[Alpha][1],J,j[1],h[j[2]]],\[CapitalPsi][z[x],\[Alpha][2],J,h[j[2]],j[3]],A[z[x],\[Mu],j[3],j[1]]},-\[Gamma][du][\[Mu],\[Alpha][1],\[Alpha][2]]\[CenterDot]{\[CapitalPsi][z[x],\[Alpha][2],J,h[j[3]],j[1]],\[CapitalPsi]b[z[x],\[Alpha][1],J,j[1],h[j[2]]],Ah[z[x],\[Mu],h[j[2]],h[j[3]]]}}]
VertexAAA[x_,j_]:=Block[{\[Mu]=Unique[\[Mu]],\[Nu]=Unique[\[Nu]],\[Rho]=Unique[\[Rho]]},{(Global`\[Kappa]/(4\[Pi]) 2/3 Global`\[Epsilon][\[Mu],\[Nu],\[Rho]])\[CenterDot]{A[z[x],\[Mu],j[1],j[2]],A[z[x],\[Nu],j[2],j[3]],A[z[x],\[Rho],j[3],j[1]]},(-(Global`\[Kappa]/(4\[Pi])) 2/3 Global`\[Epsilon][\[Mu],\[Nu],\[Rho]])\[CenterDot]{Ah[z[x],\[Mu],h[j[1]],h[j[2]]],Ah[z[x],\[Nu],h[j[2]],h[j[3]]],Ah[z[x],\[Rho],h[j[3]],h[j[1]]]}}]
VertexACC[x_,j_]:=Block[{\[Mu]=Unique[\[Mu]],J=Unique[J]},{I\[CenterDot]{C[z[x],J,j[3],h[j[1]]],d[z[x],\[Mu]]\[CenterDot]Cb[z[x],J,h[j[1]],j[2]],A[z[x],\[Mu],j[2],j[3]]},-I\[CenterDot]{d[z[x],\[Mu]]\[CenterDot]Cb[z[x],J,h[j[1]],j[2]],C[z[x],J,j[2],h[j[3]]],Ah[z[x],\[Mu],h[j[3]],h[j[1]]]},-I\[CenterDot]{d[z[x],\[Mu]]\[CenterDot]C[z[x],J,j[3],h[j[1]]],Cb[z[x],J,h[j[1]],j[2]],A[z[x],\[Mu],j[2],j[3]]},I\[CenterDot]{Cb[z[x],J,h[j[1]],j[2]],d[z[x],\[Mu]]\[CenterDot]C[z[x],J,j[2],h[j[3]]],Ah[z[x],\[Mu],h[j[3]],h[j[1]]]}}]
VertexAACC[x_,j_]:=Block[{\[Mu]=Unique[\[Mu]],J=Unique[J]},{1\[CenterDot]{C[z[x],J,j[4],h[j[1]]],Cb[z[x],J,h[j[1]],j[2]],A[z[x],\[Mu],j[2],j[3]],A[z[x],\[Mu],j[3],j[4]]},-1\[CenterDot]{C[z[x],J,j[4],h[j[1]]],Ah[z[x],\[Mu],h[j[1]],h[j[2]]],Cb[z[x],J,h[j[2]],j[3]],A[z[x],\[Mu],j[3],j[4]]},-1\[CenterDot]{Cb[z[x],J,h[j[1]],j[2]],A[z[x],\[Mu],j[2],j[3]],C[z[x],J,j[3],h[j[4]]],Ah[z[x],\[Mu],h[j[4]],h[j[1]]]},1\[CenterDot]{Ah[z[x],\[Mu],h[j[1]],h[j[2]]],Cb[z[x],J,h[j[2]],j[3]],C[z[x],J,j[3],h[j[4]]],Ah[z[x],\[Mu],h[j[4]],h[j[1]]]}}]
VertexCC\[Psi]\[Psi][x_,j_,\[Alpha]_]:=Block[{II=Unique[II],J=Unique[J],K=Unique[K],L=Unique[L]},{-((2\[Pi] I)/Global`\[Kappa])\[CenterDot]{C[z[x],II,j[2],h[j[3]]],\[CapitalPsi][z[x],\[Alpha][1],J,h[j[3]],j[4]],\[CapitalPsi]b[z[x],\[Alpha][1],J,j[4],h[j[1]]],Cb[z[x],II,h[j[1]],j[2]]},(2\[Pi] I)/Global`\[Kappa]\[CenterDot]{Cb[z[x],II,h[j[2]],j[3]],\[CapitalPsi]b[z[x],\[Alpha][1],J,j[3],h[j[4]]],\[CapitalPsi][z[x],\[Alpha][1],J,h[j[4]],j[1]],C[z[x],II,j[1],h[j[2]]]},-((4\[Pi] I)/Global`\[Kappa])\[CenterDot]{Cb[z[x],J,h[j[2]],j[3]],\[CapitalPsi]b[z[x],\[Alpha][1],II,j[3],h[j[4]]],\[CapitalPsi][z[x],\[Alpha][1],J,h[j[4]],j[1]],C[z[x],II,j[1],h[j[2]]]},(4\[Pi] I)/Global`\[Kappa]\[CenterDot]{C[z[x],J,j[2],h[j[3]]],\[CapitalPsi][z[x],\[Alpha][1],II,h[j[3]],j[4]],\[CapitalPsi]b[z[x],\[Alpha][1],J,j[4],h[j[1]]],Cb[z[x],II,h[j[1]],j[2]]},((2\[Pi] I)/Global`\[Kappa] Global`\[Epsilon]\[Epsilon][II,J,K,L])\[CenterDot]{\[CapitalPsi]b[z[x],\[Alpha][1],J,j[2],h[j[3]]],Cb[z[x],K,h[j[3]],j[4]],\[CapitalPsi]b[z[x],\[Alpha][1],L,j[4],h[j[1]]],Cb[z[x],II,h[j[1]],j[2]]},(-((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon]\[Epsilon][II,J,K,L])\[CenterDot]{\[CapitalPsi][z[x],\[Alpha][1],J,h[j[2]],j[3]],C[z[x],K,j[3],h[j[4]]],\[CapitalPsi][z[x],\[Alpha][1],L,h[j[4]],j[1]],C[z[x],II,j[1],h[j[2]]]}}]
VertexCCCCCC[x_,j_]:=Block[{II=Unique[II],J=Unique[J],K=Unique[K]},{-((4\[Pi]^2)/(3 Global`\[Kappa]^2))\[CenterDot]{C[z[x],II,j[1],h[j[2]]],Cb[z[x],II,h[j[2]],j[3]],C[z[x],J,j[3],h[j[4]]],Cb[z[x],J,h[j[4]],j[5]],C[z[x],K,j[5],h[j[6]]],Cb[z[x],K,h[j[6]],j[1]]},-((4\[Pi]^2)/(3Global`\[Kappa]^2))\[CenterDot]{Cb[z[x],II,h[j[1]],j[2]]C[z[x],II,j[2],h[j[3]]],Cb[z[x],J,h[j[3]],j[4]],C[z[x],J,j[4],h[j[5]]],Cb[z[x],K,h[j[5]],j[6]],C[z[x],K,j[6],h[j[1]]]},-((16\[Pi]^2)/(3Global`\[Kappa]^2))\[CenterDot]{C[z[x],II,j[1],h[j[2]]],Cb[z[x],J,h[j[2]],j[3]],C[z[x],K,j[3],h[j[4]]],Cb[z[x],II,h[j[4]],j[5]],C[z[x],J,j[5],h[j[6]]],Cb[z[x],K,h[j[6]],j[1]]},(24\[Pi]^2)/(3Global`\[Kappa]^2)\[CenterDot]{C[z[x],II,j[1],h[j[2]]],Cb[z[x],J,h[j[2]],j[3]],C[z[x],J,j[3],h[j[4]]],Cb[z[x],II,h[j[4]],j[5]],C[z[x],K,j[5],h[j[6]]],Cb[z[x],K,h[j[6]],j[1]]}}]
VertexAcc[x_,j_]:=Block[{\[Mu]=Unique[\[Mu]]},{(I Global`\[Kappa]/(4\[Pi]))\[CenterDot]{c[z[x],j[3],j[1]],d[z[x],\[Mu]]\[CenterDot]cb[z[x],j[1],j[2]],A[z[x],\[Mu],j[2],j[3]]},(-I Global`\[Kappa]/(4\[Pi]))\[CenterDot]{d[z[x],\[Mu]]\[CenterDot]cb[z[x],j[1],j[2]],c[z[x],j[2],j[3]],A[z[x],\[Mu],j[3],j[1]]},(-I Global`\[Kappa]/(4\[Pi]))\[CenterDot]{ch[z[x],h[j[3]],h[j[1]]],d[z[x],\[Mu]]\[CenterDot]chb[z[x],h[j[1]],h[j[2]]],Ah[z[x],\[Mu],h[j[2]],h[j[3]]]},(I Global`\[Kappa]/(4\[Pi]))\[CenterDot]{d[z[x],\[Mu]]\[CenterDot]chb[z[x],h[j[1]],h[j[2]]],ch[z[x],h[j[2]],h[j[3]]],Ah[z[x],\[Mu],h[j[3]],h[j[1]]]}}]
(* ::Section::Closed:: *)
(*Traces*)
(* Select the last indices of a field *)
ultimiindici[A_]:=A/.AA_[__,a_,b_]:>{a,b}
(* Sort the fields in order to reconstruct the trace over the gauge group indices *)
sorting[A_,r_]:=ReplaceRepeated[A,a_\[CenterDot]b_:> a\[CenterDot]If[b==={},{},If[ultimiindici[b[[r]]][[-1]]===ultimiindici[b[[r+1]]][[1]],b,{Drop[b,{r+1}],b[[r+1]]}//Flatten]]]
(* Select the part of the Wilson loop operator expansion with
s=number of fields on the loop
n=number of gauge fields (n\[LessEqual]s)
m=number of couple COverscript[C, \[Dash]] of scalar fields (m\[LessEqual]s)
UP= 1 for the upper-left sector
2 for the lower-right sector*)
Listatemp[s_,n_,UP_]:=Module[{l=List@@(Expansion[s][[UP]])},Module[{M1=Table[{a,Count[(Position[l,xp[__]]//Transpose)[[1]],a]},{a,1,Length[l]}]},List@(l//Delete[#,Table[If[M1[[p,2]]===n,{0},{M1[[p,1]]}],{p,1,Length[M1]}]]&)]]
Lista[s_,n_,m_,UP_]:=Module[{l=Listatemp[s,n,UP]},Module[{M1=Table[{a,Count[(Flatten[{Position[l,Global`Mh[__]],Position[l,Global`M[__]]},1]//Transpose)[[1]],a]},{a,1,Length[l]}]},List@(l//Delete[#,Table[If[M1[[p,2]]===m,{0},{M1[[p,1]]}],{p,1,Length[M1]}]]&)]]
Loopaux[s_,n_,m_,UP_]:=Module[{B=Lista[s,n,m,UP]},Table[(B[[q]]/.\[Psi][__]->1/.\[Psi]b[__]->1/.A[__]->1/.Ah[__]->1/.C[__]->1/.Cb[__]->1)\[CenterDot]If[s===1&&m===0,List@(B[[q]]/(B[[q]]/.\[Psi][__]->1/.\[Psi]b[__]->1/.A[__]->1/.Ah[__]->1/.C[__]->1/.Cb[__]->1)),List@@(B[[q]]/(B[[q]]/.\[Psi][__]->1/.\[Psi]b[__]->1/.A[__]->1/.Ah[__]->1/.C[__]->1/.Cb[__]->1))],{q,1,Length[B]}]]
auxilliary={i[1],h[i[1]]};
Loopsorted[s_,n_,m_,UP_]:=Module[{l=Fold[sorting,Loopaux[s,n,m,UP],Table[k,{k,1,s+m-1}]]},If[l==={{}\[CenterDot]{}},0,Module[{p=Position[l/.a_\[CenterDot]b_:>Table[ultimiindici[b[[u]]],{u,1,Length[b]}],{auxilliary[[UP]],__}]},Table[l[[q]]/.a_\[CenterDot]b_:>a\[CenterDot]RotateLeft[b,p[[q,2]]-1],{q,1,Length[l]}]]]]//Quiet
(* Merge the selected vertices with the previously selected the part of the Wilson loop operator expansion
The entries are the same of the previous functions with the following addition
V1=number of vertices VertexA\[Psi]\[Psi]
V2=number of vertices VertexAAA
V3=number of vertices VertexACC
V4=number of vertices VertexAACC
V5=number of vertices VertexCC\[Psi]\[Psi]
V6=number of vertices VertexCCCCCC
V7=number of vertices VertexAcc*)
Lorentzaux={\[Alpha],\[Beta],\[Zeta],\[Xi],\[Chi],\[Iota],\[Upsilon],\[Omicron]};
Rsymaux={j,k,l,g,t,w,b,u};
indexaux={\[Alpha]\[Alpha],\[Beta]\[Beta],\[Zeta]\[Zeta],\[Xi]\[Xi],\[Chi]\[Chi],\[Iota]\[Iota],\[Upsilon]\[Upsilon],\[Omicron]\[Omicron]};
Rsymaux2={j_,k_,l_,g_,t_,w_,b_,u_};
indexaux2={\[Alpha]\[Alpha]_,\[Beta]\[Beta]_,\[Zeta]\[Zeta]_,\[Xi]\[Xi]_,\[Chi]\[Chi]_,\[Iota]\[Iota]_,\[Upsilon]\[Upsilon]_,\[Omicron]\[Omicron]_};
Tracce[s_,n_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,UP_]:=Module[{ls=Loopsorted[s,n,m,UP]},Table[Flatten[{Table[VertexA\[Psi]\[Psi][dd,Rsymaux[[dd]],Lorentzaux[[dd]]][[indexaux[[dd]]]],{dd,1,V1}],Table[VertexAAA[dd,Rsymaux[[dd]]][[indexaux[[dd]]]],{dd,V1+1,V2+V1}],Table[VertexACC[dd,Rsymaux[[dd]]][[indexaux[[dd]]]],{dd,V1+V2+1,V2+V1+V3}],Table[VertexAACC[dd,Rsymaux[[dd]]][[indexaux[[dd]]]],{dd,V1+V2+V3+1,V2+V1+V3+V4}],Table[VertexCC\[Psi]\[Psi][dd,Rsymaux[[dd]],Lorentzaux[[dd]]][[indexaux[[dd]]]],{dd,V1+V2+V3+V4+1,V2+V1+V3+V4+V5}],Table[VertexCCCCCC[dd,Rsymaux[[dd]]][[indexaux[[dd]]]],{dd,V1+V2+V3+V4+V5+1,V2+V1+V3+V4+V5+V6}],Table[VertexAcc[dd,Rsymaux[[dd]]][[indexaux[[dd]]]],{dd,V1+V2+V3+V4+V5+V6+1,V2+V1+V3+V4+V5+V6+V7}],ls[[\[Sigma]\[Sigma]]]}],##]&@@Insert[Flatten[{Table[{indexaux[[q]],1,2},{q,1,V1+V2}],Table[{indexaux[[q]],1,4},{q,V1+V2+1,V1+V2+V3+V4}],Table[{indexaux[[q]],1,6},{q,V1+V2+V3+V4+1,V1+V2+V3+V4+V5}],Table[{indexaux[[q]],1,4},{q,V1+V2+V3+V4+V5+1,V1+V2+V3+V4+V5+V6+V7}]},1],{\[Sigma]\[Sigma],1,Length[ls]},-1]]/.-(a_\[CenterDot]b_):>(-a)\[CenterDot]b/.Table[Rsymaux2[[dd]]\[CenterDot]indexaux2[[dd]],{dd,1,1+V1+V2+V3+V4+V5+V6+V7}]->((-1)^(V1+V2+V3+V4+V5+V6+V7)/(V1!V2!V3!V4!V5!V6!V7!) Product[Rsymaux[[dd]],{dd,1,1+V1+V2+V3+V4+V5+V6+V7}])\[CenterDot]Table[indexaux[[dd]],{dd,1,1+V1+V2+V3+V4+V5+V6+V7}]
(* Select the parts of the output of Tracce that are non vanishing counting if the number of a certain field is even (otherwise the wick contractions give zero)*)
Zerocheck[w_]:=Module[{pp=w/.a_ \[CenterDot] b_:>Flatten[b]},If[Count[pp,\[Psi][__]]+Count[pp,\[CapitalPsi][__]]===Count[pp,\[CapitalPsi]b[__]]+Count[pp,\[Psi]b[__]]&&Count[pp,C[__]]+Count[pp,d[__]\[CenterDot]C[__]]===Count[pp,Cb[__]]+Count[pp,d[__]\[CenterDot]Cb[__]]&&Count[pp,c[__]]+Count[pp,d[__]\[CenterDot]c[__]]===Count[pp,cb[__]]+Count[pp,d[__]\[CenterDot]cb[__]]&&Count[pp,ch[__]]+Count[pp,d[__]\[CenterDot]ch[__]]===Count[pp,chb[__]]+Count[pp,d[__]\[CenterDot]chb[__]]&&EvenQ[Count[pp,A[__]]]&&EvenQ[Count[pp,Ah[__]]],OK,0]]
Nonvanishingtrace[s_,n_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,UP_]:=Module[{p0=Flatten[Tracce[s,n,m,V1,V2,V3,V4,V5,V6,V7,UP]]},Module[{p=Position[Zerocheck/@p0,OK]},p0[[#]]&@Flatten[p]]]
(* ::Section::Closed:: *)
(*Rules*)
(* definition of propagators in terms of \[CapitalDelta] *)
prop[\[Mu]_]:={\[LeftAngleBracket]A[z[a_],b_,c_,d1_],A[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[z[a],\[Xi]]\[CenterDot]\[CapitalDelta]a[z[a],x[\[Tau][\[Alpha]]]]],\[LeftAngleBracket]A[\[Tau][a_],b_,c_,d1_],A[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[x[\[Tau][a]],\[Xi]]\[CenterDot]\[CapitalDelta]a[x[\[Tau][a]],z[\[Alpha]]]],
\[LeftAngleBracket]A[z[a_],b_,c_,d1_],A[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[z[a],\[Xi]]\[CenterDot]\[CapitalDelta]a[z[a],z[\[Alpha]]]],\[LeftAngleBracket]A[\[Tau][a_],b_,c_,d1_],A[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[x[\[Tau][a]],\[Xi]]\[CenterDot]\[CapitalDelta]a[x[\[Tau][a]],x[\[Tau][\[Alpha]]]]],\[LeftAngleBracket]Ah[z[a_],b_,c_,d1_],Ah[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[z[a],\[Xi]]\[CenterDot]\[CapitalDelta]a[z[a],x[\[Tau][\[Alpha]]]]],\[LeftAngleBracket]Ah[\[Tau][a_],b_,c_,d1_],Ah[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[x[\[Tau][a]],\[Xi]]\[CenterDot]\[CapitalDelta]a[x[\[Tau][a]],z[\[Alpha]]]],
\[LeftAngleBracket]Ah[z[a_],b_,c_,d1_],Ah[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[z[a],\[Xi]]\[CenterDot]\[CapitalDelta]a[z[a],z[\[Alpha]]]],\[LeftAngleBracket]Ah[\[Tau][a_],b_,c_,d1_],Ah[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]((2\[Pi] I)/Global`\[Kappa])Global`\[Epsilon][b,\[Beta],\[Xi]]d[x[\[Tau][a]],\[Xi]]\[CenterDot]\[CapitalDelta]a[x[\[Tau][a]],x[\[Tau][\[Alpha]]]]],\[LeftAngleBracket]\[Psi][a_,b_,e_,c_,d1_],\[Psi]b[\[Alpha]_,\[Beta]_,\[Omega]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-I \[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[e,\[Omega]]\[Gamma][ud][\[Xi],b,\[Beta]]d[x[a],\[Xi]]\[CenterDot]\[CapitalDelta]f[x[a],x[\[Alpha]]]],\[LeftAngleBracket]\[Psi][a_,b_,e_,c_,d1_],\[CapitalPsi]b[\[Alpha]_,\[Beta]_,\[Omega]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-I \[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[e,\[Omega]]\[Gamma][uu][\[Xi],b,\[Beta]]d[x[a],\[Xi]]\[CenterDot]\[CapitalDelta]f[x[a],\[Alpha]]],\[LeftAngleBracket]\[CapitalPsi][a_,b_,e_,c_,d1_],\[Psi]b[\[Alpha]_,\[Beta]_,\[Omega]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-I \[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[e,\[Omega]]\[Gamma][dd][\[Xi],b,\[Beta]]d[a,\[Xi]]\[CenterDot]\[CapitalDelta]f[a,x[\[Alpha]]]],\[LeftAngleBracket]\[CapitalPsi][a_,b_,e_,c_,d1_],\[CapitalPsi]b[\[Alpha]_,\[Beta]_,\[Omega]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>Module[{\[Xi]=Unique[\[Mu]]},-I \[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[e,\[Omega]]\[Gamma][du][\[Xi],b,\[Beta]]d[a,\[Xi]]\[CenterDot]\[CapitalDelta]f[a,\[Alpha]]],\[LeftAngleBracket]C[\[Tau][a_],b_,c_,d_],Cb[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]\[CapitalDelta]c[x[\[Tau][a]],x[\[Tau][\[Alpha]]]],\[LeftAngleBracket]C[\[Tau][a_],b_,c_,d_],Cb[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]\[CapitalDelta]c[x[\[Tau][a]],z[\[Alpha]]],\[LeftAngleBracket]C[z[a_],b_,c_,d_],Cb[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]\[CapitalDelta]c[z[a],x[\[Tau][\[Alpha]]]],\[LeftAngleBracket]C[z[a_],b_,c_,d_],Cb[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]\[CapitalDelta]c[z[a],z[\[Alpha]]],\[LeftAngleBracket]C[\[Tau][a_],b_,c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]Cb[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]c[x[\[Tau][a]],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]1_]\[CenterDot]C[z[a_],b_,c_,d1_],Cb[\[Tau][\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]d[z[a],\[Mu]1]\[CenterDot]\[CapitalDelta]c[z[a],x[\[Tau][\[Alpha]]]],\[LeftAngleBracket]C[z[a_],b_,c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]Cb[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]c[z[a],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]1_]\[CenterDot]C[z[a_],b_,c_,d1_],Cb[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]d[z[a],\[Mu]1]\[CenterDot]\[CapitalDelta]c[z[a],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]2_]\[CenterDot]C[z[a_],b_,c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]Cb[z[\[Alpha]_],\[Beta]_,\[Chi]_,\[Rho]_]\[RightAngleBracket]:>\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]\[Delta]\[Delta]1[b,\[Beta]]d[z[a],\[Mu]2]\[CenterDot]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]c[z[a],z[\[Alpha]]],\[LeftAngleBracket]c[z[a_],c_,d_],cb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>-((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d,\[Chi]]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]ch[z[a_],c_,d_],chb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d,\[Chi]]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]c[z[a_],c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]cb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>-((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]1_]\[CenterDot]c[z[a_],c_,d1_],cb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>-((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]d[z[a],\[Mu]1]\[CenterDot]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]2_]\[CenterDot]c[z[a_],c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]cb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>-((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]d[z[a],\[Mu]2]\[CenterDot]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]ch[z[a_],c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]chb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]1_]\[CenterDot]ch[z[a_],c_,d1_],chb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]d[z[a],\[Mu]1]\[CenterDot]\[CapitalDelta]cc[z[a],z[\[Alpha]]],\[LeftAngleBracket]d[z[a_],\[Mu]2_]\[CenterDot]ch[z[a_],c_,d1_],d[z[\[Alpha]_],\[Mu]1_]\[CenterDot]chb[z[\[Alpha]_],\[Chi]_,\[Rho]_]\[RightAngleBracket]:>((4\[Pi])/Global`\[Kappa])\[Delta]\[Delta][c,\[Rho]]\[Delta]\[Delta][d1,\[Chi]]d[z[a],\[Mu]2]\[CenterDot]d[z[\[Alpha]],\[Mu]1]\[CenterDot]\[CapitalDelta]cc[z[a],z[\[Alpha]]]};
(* substitution rules to set to zero the vanishing Wick contractions *)
rulesprop[in_]:=Which[in===2,{\[LeftAngleBracket]A[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],chb[__]\[RightAngleBracket]->0\[LeftAngleBracket]ch[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[a_,b_,c_,d_],Cb[a_,\[Beta]_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]C[a_,b_,c_,d_],d[__]\[CenterDot]Cb[a_,\[Beta]_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]C[a_,b_,c_,d_],Cb[a_,\[Beta]_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]d[__]\[CenterDot]C[a_,b_,c_,d_],d[__]\[CenterDot]Cb[a_,\[Beta]_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]\[Psi][a_,__],\[Psi]b[a_,__]\[RightAngleBracket]:> 0,\[LeftAngleBracket]\[CapitalPsi][a_,__],\[CapitalPsi]b[a_,__]\[RightAngleBracket]:> 0,\[LeftAngleBracket]A[a_,__],A[a_,__]\[RightAngleBracket]:> 0,\[LeftAngleBracket]Ah[a_,__],Ah[a_,__]\[RightAngleBracket]:> 0,\[LeftAngleBracket]d[__]\[CenterDot]c[a_,c_,d_],cb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]c[a_,c_,d_],d[__]\[CenterDot]cb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]c[a_,c_,d_],cb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]d[__]\[CenterDot]c[a_,c_,d_],d[__]\[CenterDot]cb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]d[__]\[CenterDot]ch[a_,c_,d_],chb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]ch[a_,c_,d_],d[__]\[CenterDot]chb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]ch[a_,c_,d_],chb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0,\[LeftAngleBracket]d[__]\[CenterDot]ch[a_,c_,d_],d[__]\[CenterDot]chb[a_,\[Phi]_,\[Lambda]_]\[RightAngleBracket]:> 0},in===1,{\[LeftAngleBracket]A[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],chb[__]\[RightAngleBracket]->0\[LeftAngleBracket]ch[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0},\[LeftAngleBracket]cb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],C[__]\[RightAngleBracket]->0,
\[LeftAngleBracket]C[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]c[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]cb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]c[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]chb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]ch[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]C[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]C[__],d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]Cb[__],d[__]\[CenterDot]d[__]\[CenterDot]Cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]C[__],d[__]\[CenterDot]d[__]\[CenterDot]C[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]cb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]cb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]c[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]c[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],A[__]\[RightAngleBracket]->0,\[LeftAngleBracket]A[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],Ah[__]\[RightAngleBracket]->0,\[LeftAngleBracket]Ah[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[Psi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi][__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[Psi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[Psi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[CapitalPsi][__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi][__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]chb[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]chb[__]\[RightAngleBracket]->0,\[LeftAngleBracket]d[__]\[CenterDot]d[__]\[CenterDot]ch[__],\[CapitalPsi]b[__]\[RightAngleBracket]->0,\[LeftAngleBracket]\[CapitalPsi]b[__],d[__]\[CenterDot]d[__]\[CenterDot]ch[__]\[RightAngleBracket]->0]
(* substitution rules for the color and R-symmetry kroneker deltas *)
rule\[Delta]\[Delta]:={\[Delta]\[Delta][a_,b_]\[Delta]\[Delta][b_,c_]:>\[Delta]\[Delta][a,c],\[Delta]\[Delta]1[a_,b_]\[Delta]\[Delta]1[b_,c_]:>\[Delta]\[Delta]1[a,c],\[Delta]\[Delta][h[a_],h[b_]]/;a===b:>Global`\[CapitalMu],\[Delta]\[Delta][h[a_],h[b_]]^2/;a=!=b:>Global`\[CapitalMu],\[Delta]\[Delta][a_,b_]/;a===b:>Global`\[CapitalNu],\[Delta]\[Delta][a_,b_]^2/;a=!=b:>Global`\[CapitalNu],\[Delta]\[Delta]1[a_,b_]\[Eta][\[Tau][c_],d_,b_]:>\[Eta][\[Tau][c],d,a],\[Delta]\[Delta]1[a_,b_]\[Eta]b[\[Tau][c_],d_,b_]:>\[Eta]b[\[Tau][c],d,a],\[Delta]\[Delta]1[a_,a_]:>4,\[Delta]\[Delta]1[a_,b_]Global`M[Global`\[Tau][c_],d_,a_]:>Global`M[Global`\[Tau][c],d,b],\[Delta]\[Delta]1[a_,b_]Global`Mh[Global`\[Tau][c_],d_,a_]:>Global`Mh[Global`\[Tau][c],d,b],\[Delta]\[Delta]1[a_,b_]Global`M[Global`\[Tau][c_],b_,d_]:>Global`M[Global`\[Tau][c],a,d],\[Delta]\[Delta]1[a_,b_]Global`Mh[Global`\[Tau][c_],b_,d_]:>Global`Mh[Global`\[Tau][c],a,d],\[Delta]\[Delta]1[a_,b_]Global`\[Epsilon]\[Epsilon][a_,c_,d_,e_]:>Global`\[Epsilon]\[Epsilon][b,c,d,e],\[Delta]\[Delta]1[a_,b_]Global`\[Epsilon]\[Epsilon][c_,a_,d_,e_]:>Global`\[Epsilon]\[Epsilon][c,b,d,e],\[Delta]\[Delta]1[a_,b_]Global`\[Epsilon]\[Epsilon][d_,c_,a_,e_]:>Global`\[Epsilon]\[Epsilon][d,c,b,e],\[Delta]\[Delta]1[a_,b_]Global`\[Epsilon]\[Epsilon][e_,c_,d_,a_]:>Global`\[Epsilon]\[Epsilon][e,c,d,b],\[Delta]\[Delta]1[a_,b_]^2/;a=!=b:>4,\[Delta]\[Delta]1[a_,b_]Global`nJ[Global`\[Tau][c_],b_]:>Global`nJ[Global`\[Tau][c],a],\[Delta]\[Delta]1[a_,b_]Global`nJb[Global`\[Tau][c_],b_]:>Global`nJb[Global`\[Tau][c],a]};
(* substitution rules to contract the Grassmann couplings and the Dirac matrices *)
rule\[Eta]:={S_. \[Gamma][p_][\[Mu]_,\[Alpha]_,\[Alpha]_]:> S Global`\[Gamma][\[Mu]],S_. \[Eta][\[Tau][a_],\[Beta]_,J_]\[Eta]b[\[Tau][b_],\[Beta]_,K_]:>S Global`nJ[Global`\[Tau][a],J]Global`nJb[Global`\[Tau][b],K]Global`\[Eta][x[\[Tau][a]]]\[CenterDot]Global`\[Eta]b[x[\[Tau][b]]],S_. \[Eta][\[Tau][a_],\[Beta]_,J_]\[Gamma][q_][\[Mu]_,\[Beta]_,t_]:>S Global`nJ[Global`\[Tau][a],J](\[Eta][x[\[Tau][a]]]**Global`\[Gamma][\[Mu]])[t],S_. \[Eta][\[Tau][a_],\[Beta]_,J_]\[Gamma][q_][\[Mu]_,t_,\[Beta]_]:>S Global`nJ[Global`\[Tau][a],J](Global`\[Eta][x[\[Tau][a]]]**Global`\[Gamma][\[Mu]])[t],S_. A_[\[Beta]_]\[Gamma][q_][\[Mu]_,t_,\[Beta]_]:>S (A**Global`\[Gamma][\[Mu]])[t],S_. A_[\[Beta]_]\[Gamma][q_][\[Mu]_,\[Beta]_,t_]:>S (A**Global`\[Gamma][\[Mu]])[t],S_. A___[\[Beta]_]\[Eta]b[\[Tau][b_],\[Beta]_,K_]:>S Global`nJb[Global`\[Tau][b],K]A**Global`\[Eta]b[x[\[Tau][b]]],S_. \[Gamma][p_][\[Mu]_,t_,\[Beta]_]\[Gamma][q_][\[Nu]_,\[Beta]_,t_]:>S Global`\[Gamma][\[Mu]]\[CenterDot]Global`\[Gamma][\[Nu]],S_. \[Gamma][p_][\[Mu]_,t_,\[Beta]_]\[Gamma][q_][\[Nu]_,t_,\[Beta]_]:>S Global`\[Gamma][\[Mu]]\[CenterDot]Global`\[Gamma][\[Nu]],S_. A_[\[Delta]_,\[Beta]_]\[Gamma][q_][\[Mu]_,\[Delta]_,\[Beta]_]:>S A**Global`\[Gamma][\[Mu]],S_. A_[\[Delta]_,\[Beta]_]\[Gamma][q_][\[Mu]_,\[Beta]_,\[Delta]_]:>S A**Global`\[Gamma][\[Mu]],S_. \[Gamma][p_][\[Mu]_,t_,\[Beta]_]\[Gamma][q_][\[Nu]_,\[Beta]_,s_]:>S (Global`\[Gamma][\[Mu]]**Global`\[Gamma][\[Nu]])[t,s],S_. A_[\[Delta]_,\[Beta]_]\[Gamma][q_][\[Mu]_,\[Beta]_,\[Alpha]_]:>S (A**Global`\[Gamma][\[Mu]])[\[Delta],\[Alpha]],S_. \[Gamma][p_][\[Mu]_,t_,\[Beta]_]\[Gamma][q_][\[Nu]_,s_,\[Beta]_]:>S (Global`\[Gamma][\[Mu]]**Global`\[Gamma][\[Nu]])[t,s],S_. A_[\[Delta]_,\[Beta]_]\[Gamma][q_][\[Mu]_,\[Alpha]_,\[Beta]_]:>S (A**Global`\[Gamma][\[Mu]])[\[Delta],\[Alpha]],S_. A_[\[Delta]_,\[Beta]_]B_[\[Delta]_,\[Beta]_]:>S A**B,S_. A_[\[Delta]_,\[Beta]_]B_[\[Beta]_,\[Delta]_]:>S A**B,S_. A_[\[Delta]_,\[Beta]_]B_[\[Beta]_,w_]/;Head[A]=!=Global`nJ&&Head[A]=!=Global`nJb&&Head[B]=!=Global`nJ&&Head[B]=!=Global`nJb:>S ( A**B)[\[Delta],w],S_. A_[\[Delta]_,\[Beta]_]B_[w_,\[Beta]_]/;Head[A]=!=Global`nJ&&Head[A]=!=Global`nJb&&Head[B]=!=Global`nJ&&Head[B]=!=Global`nJb:>S (A**B)[\[Delta],w]}
(* substitution rules to contract the reduced couplings n and the coupling matrices M *)
ruleMn:={S_. Global`M[Global`\[Tau][a_],\[Alpha]_,\[Alpha]_]:>S Global`M[Global`\[Tau][a]],S_. Global`Mh[Global`\[Tau][a_],\[Alpha]_,\[Alpha]_]:>S Global`Mh[Global`\[Tau][a]],S_. Global`nJ[Global`\[Tau][a_],J_]Global`nJb[Global`\[Tau][b_],J_]:>S Global`nJ[Global`\[Tau][a]]\[CenterDot]Global`nJb[Global`\[Tau][b]],S_. Global`nJb[Global`\[Tau][a_],J_]Global`M[Global`\[Tau][b_],J_,L_]:>S (Global`nJb[Global`\[Tau][a]]**Global`M[Global`\[Tau][b]])[L],S_. Global`nJb[Global`\[Tau][a_],J_]Global`Mh[Global`\[Tau][b_],J_,L_]:>S (Global`nJb[Global`\[Tau][a]]**Global`Mh[Global`\[Tau][b]])[L],S_. A_[\[Beta]_]Global`M[Global`\[Tau][a_],\[Beta]_,L_]:>S (A**Global`M[Global`\[Tau][a]])[L],S_. A_[\[Beta]_]Global`Mh[Global`\[Tau][a_],\[Beta]_,L_]:>S (A**Global`M[h\[Tau][a]])[L],S_. A_[J_] Global`nJ[Global`\[Tau][a_],J_]:>S A**Global`nJ[Global`\[Tau][a]],S_. Global`M[Global`\[Tau][a_],t_,\[Beta]_]Global`M[Global`\[Tau][b_],\[Beta]_,t_]:>S Global`M[Global`\[Tau][a]]\[CenterDot]Global`M[Global`\[Tau][b]],S_. Global`Mh[Global`\[Tau][a_],t_,\[Beta]_]Global`Mh[Global`\[Tau][b_],\[Beta]_,t_]:>S Global`Mh[Global`\[Tau][a]]\[CenterDot]Global`Mh[Global`\[Tau][b]],S_. Global`Mh[Global`\[Tau][a_],t_,\[Beta]_]Global`M[Global`\[Tau][b_],\[Beta]_,t_]:>S Global`Mh[Global`\[Tau][a]]\[CenterDot]Global`M[Global`\[Tau][b]],S_. Global`M[Global`\[Tau][a_],t_,\[Beta]_]Global`Mh[Global`\[Tau][b_],\[Beta]_,t_]:>S Global`M[Global`\[Tau][a]]\[CenterDot]Global`Mh[Global`\[Tau][b]],S_. A_[\[Delta]_,\[Beta]_]Global`M[Global`\[Tau][a_],\[Beta]_,\[Delta]_]:>S (A**Global`M[Global`\[Tau][a]]),S_. A_[\[Delta]_,\[Beta]_]Global`Mh[Global`\[Tau][a_],\[Beta]_,\[Delta]_]:>S (A**Global`Mh[Global`\[Tau][a]]),S_. Global`M[Global`\[Tau][a_],t_,\[Beta]_]Global`M[Global`\[Tau][b_],\[Beta]_,s_]:>S (Global`M[Global`\[Tau][a]]**Global`M[Global`\[Tau][b]])[t,s],S_. Global`Mh[Global`\[Tau][a_],t_,\[Beta]_]Global`Mh[Global`\[Tau][b_],\[Beta]_,s_]:>S (Global`Mh[Global`\[Tau][a]]**Global`Mh[Global`\[Tau][b]])[t,s],S_. Global`Mh[Global`\[Tau][a_],t_,\[Beta]_]Global`M[Global`\[Tau][b_],\[Beta]_,s_]:>S (Global`Mh[Global`\[Tau][a]]**Global`M[Global`\[Tau][b]])[t,s],S_. Global`M[Global`\[Tau][a_],t_,\[Beta]_]Global`Mh[Global`\[Tau][b_],\[Beta]_,s_]:>S (Global`M[Global`\[Tau][a]]**Global`Mh[Global`\[Tau][b]])[t,s],S_. A_[\[Delta]_,\[Beta]_]Global`M[Global`\[Tau][a_],\[Beta]_,\[Alpha]_]:>S (A**Global`M[Global`\[Tau][a]])[\[Delta],\[Alpha]],S_. A_[\[Delta]_,\[Beta]_]Global`Mh[Global`\[Tau][a_],\[Beta]_,\[Alpha]_]:>S (A**Global`Mh[Global`\[Tau][a]])[\[Delta],\[Alpha]],S_. A_[\[Delta]_,\[Beta]_]B_[\[Beta]_,\[Delta]_]/;A=!=Global`\[CapitalDelta]&&B=!=Global`\[CapitalDelta]:>S A**B}
(* substitution rules to rename the indices of gamma matrices and epsilon tensors *)
relabelling\[Gamma][S_]:=Table[S[[i]]/.With[{x=(List@@((S[[i]]/.CenterDot[a__]:>Times[a])/(S[[i]]/.CenterDot[a__]:>Times[a]/.Global`\[Gamma][__]:>1)))/.Global`\[Gamma][a_]:>a},Table[x[[j]]->Global`\[Sigma][j],{j,1,Length[x]}]],{i,1,Length[S]}]
relabelling\[Epsilon][S_]:=Table[S[[i]]/.With[{x=(S[[i]]/(S[[i]]/.Global`\[Epsilon][__]:>1))},If[x===1,{},With[{xx=DeleteDuplicates[(List@@(x/.Global`\[Epsilon][a___]^b_:>Global`\[Epsilon][a]))/.Global`\[Epsilon][a___]:>a]},Table[xx[[j]]->Global`\[Mu][j],{j,1,Length[xx]}]]]],{i,1,Length[S]}]
relabelling\[Epsilon]\[Epsilon][S_]:=Table[S[[i]]/.With[{x=(S[[i]]/(S[[i]]/.Global`\[Epsilon]\[Epsilon][__]:>1))},If[x===1,{},With[{xx=DeleteDuplicates[(List@@(x/.Global`\[Epsilon]\[Epsilon][a___]^b_:>Global`\[Epsilon]\[Epsilon][a]))/.Global`\[Epsilon]\[Epsilon][a___]:>a]},Table[xx[[j]]->Global`J[j],{j,1,Length[xx]}]]]],{i,1,Length[S]}]
(* Check if one diagram contains tadpoles
tad= 1 tadpoles option activated
2 tadpoles option deactivated*)
\[CapitalDelta]csubs[W_,m_]:=Module[{ppp=Module[{pp2=Module[{pp=Module[{p2=Module[{p=W/.A_. \[CapitalDelta]c[x[a_],x[\[Beta]_]]^2:>A \[CapitalDelta]c[z[m],x[\[Beta]]]^2 \[CapitalDelta]f[x[a],z[m]]},If[p===W,p/.A_. \[CapitalDelta]c[x[a_],z[\[Beta]_]]^2:>A \[CapitalDelta]c[z[m],z[\[Beta]]]^2 \[CapitalDelta]f[x[a],z[m]],Return[p]]]},If[p2===W,p2/.A_. \[CapitalDelta]c[z[a_],x[\[Beta]_]]^2:>A \[CapitalDelta]c[z[a],z[m]]^2 \[CapitalDelta]f[z[m],x[\[Beta]]],Return[p2]]]},If[pp===W,pp/.A_. \[CapitalDelta]c[x[a_],\[Beta]_]\[CapitalDelta]c[x[a_],\[Gamma]_]:>A \[CapitalDelta]c[z[m],\[Beta]]\[CapitalDelta]c[z[m],\[Gamma]]\[CapitalDelta]f[x[a],z[m]],Return[pp]]]},If[pp2===W,pp2/.A_. \[CapitalDelta]c[\[Beta]_,x[a_]]\[CapitalDelta]c[\[Gamma]_,x[a_]]:>A \[CapitalDelta]c[\[Beta],z[m]]\[CapitalDelta]c[\[Gamma],z[m]]\[CapitalDelta]f[z[m],x[a]],Return[pp2]]]},If[ppp===W,ppp/.A_. \[CapitalDelta]c[\[Beta]_,x[a_]]\[CapitalDelta]c[x[a_],\[Gamma]_]:>A \[CapitalDelta]c[\[Beta],z[m]]\[CapitalDelta]c[z[m],\[Gamma]]\[CapitalDelta]f[z[m],x[a]],Return[ppp]]]
\[CapitalDelta]ccheck[W_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_]:=Fold[\[CapitalDelta]csubs,W,Table[i,{i,V1+V2+V3+V4+V5+V6+V7+1,V1+V2+V3+V4+V5+V6+V7+m}]]
CountTadpole[A_,s_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,tad_]:=If[tad===2,If[Head[A]===Plus,Module[{AA=List@@A},Plus@@Table[If[MemberQ[Table[ConnectedGraphQ[VertexDelete[Graph[({(List@@\[CapitalDelta]ccheck[((AA[[j]]//.CenterDot[a__]:>Times[a])/((AA[[j]]//.CenterDot[a__]:>Times[a])/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>1)),m,V1,V2,V3,V4,V5,V6,V7]/.\[CapitalDelta]cc[a_,b_]^q_:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]c[a_,b_]^q_:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]},Table[{x[\[Tau][i]]<->x[\[Tau][i+1]]},{i,1,s-1}]}//Flatten)/.z[a_]:>a],qq]],{qq,1,V1+V2+V3+V4+V5+V6+V7+m}],False],0,AA[[j]]],{j,1,Length[AA]}]],If[MemberQ[Table[ConnectedGraphQ[VertexDelete[Graph[({(List@@\[CapitalDelta]ccheck[((A//.CenterDot[a__]:>Times[a])/((A//.CenterDot[a__]:>Times[a])/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>1)),m,V1,V2,V3,V4,V5,V6,V7]/.\[CapitalDelta]cc[a_,b_]^q_:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]c[a_,b_]^q_:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]},Table[{x[\[Tau][i]]<->x[\[Tau][i+1]]},{i,1,s-1}]}//Flatten)/.z[a_]:>a],qq]],{qq,1,V1+V2+V3+V4+V5+V6+V7+m}],False],0,A]],
If[Head[A]===Plus,Module[{AA=List@@A},Plus@@Table[Connected[AA[[j]],s],{j,1,Length[AA]}]],Connected[A,s]]]
Connected[aa_,s_]:=Module[{p=((aa//.CenterDot[a__]:>Times[a])/((aa//.CenterDot[a__]:>Times[a])/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>1))},If[Head[p]===Times,If[ConnectedGraphQ[Graph[({((List@@p)/.\[CapitalDelta]c[a_,b_]^q_:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]cc[a_,b_]^q_:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]},Table[{x[\[Tau][i]]<->x[\[Tau][i+1]]},{i,1,s-1}]}//Flatten)]],aa,0],If[ConnectedGraphQ[Graph[({((List@p)/.\[CapitalDelta]c[a_,b_]^q_:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]cc[a_,b_]^q_:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]<->\[Beta]},Table[{x[\[Tau][i]]<->x[\[Tau][i+1]]},{i,1,s-1}]}//Flatten)]],aa,0]]]
(* Check if one diagram contains self-energies
SE= 1 Self-energies option activated
2 Self-energies option deactivated*)
SELFEN[es_]:=Module[{a1=FindEdgeCut[Graph[es]]},Which[Length[a1]===2,"SELF",Length[a1]===1,Module[{a2=Delete[es,Position[es,Sequence@@a1]]},
Module[{a3=Select[WeaklyConnectedComponents[a2//Graph],Length[#]>1&]},EdgeList/@Table[Subgraph[Graph[a2],a3[[i]]],{i,1,Length[a3]}]]],True,{}]]
SEcheck[A_,SE_]:=If[SE===2,If[Head[A]===Plus,Module[{AA=List@@A},Module[{pp=Table[(List@@((AA[[j]]//.CenterDot[a__]:>Times[a])/((AA[[j]]//.CenterDot[a__]:>Times[a])/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>1))/.\[CapitalDelta]cc[a_,b_]^q_:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]c[a_,b_]^q_:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[x[\[Alpha]_],x[\[Beta]_]]:>{}/.\[CapitalDelta]f[x[\[Alpha]_],x[\[Beta]_]]:>{}/.\[CapitalDelta]c[x[\[Alpha]_],x[\[Beta]_]]:>{}/.\[CapitalDelta]f[z[\[Alpha]_],x[\[Beta]_]]:>{z[\[Alpha]]<->\[FilledSquare]}/.\[CapitalDelta]f[x[\[Alpha]_],z[\[Beta]_]]:>{\[FilledSquare]<->z[\[Beta]]}/.\[CapitalDelta]f[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}/.\[CapitalDelta]a[x[\[Alpha]_],z[\[Beta]_]]:>{\[FilledSquare]<->z[\[Beta]]}/.\[CapitalDelta]a[z[\[Alpha]_],x[\[Beta]_]]:>{z[\[Alpha]]<->\[FilledSquare]}/.\[CapitalDelta]a[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}/.\[CapitalDelta]c[x[\[Alpha]_],z[\[Beta]_]]:>{\[FilledSquare]<->z[\[Beta]]}/.\[CapitalDelta]c[z[\[Alpha]_],x[\[Beta]_]]:>{z[\[Alpha]]<->\[FilledSquare]}/.\[CapitalDelta]c[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}/.\[CapitalDelta]cc[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}//Flatten,{j,1,Length[AA]}]},Plus@@Table[Which[pp[[h]]==={},AA[[h]],MemberQ[Module[{matr=Graph[pp[[h]]]//IncidenceMatrix//Normal},Table[MemberQ[matr[[j]],1]&&MemberQ[matr[[j]],2]&&Plus@@matr[[j]]===4,{j,1,Length[matr]}]],True],0,True,Module[{test=NestWhile[Flatten[Map[SELFEN,#],1]&,SELFEN[pp[[h]]],(FreeQ[#,"SELF"]&&Length[#]>0)& ]},Which[test==={},AA[[h]],MemberQ[Flatten[{test}],"SELF"],0]]],{h,1,Length[pp]}]]],Module[{pp=(Module[{ss=((A//.CenterDot[a__]:>Times[a])/((A//.CenterDot[a__]:>Times[a])/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>1/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>1))},If[Head[ss]===Times,List@@ss,{ss}]]/.\[CapitalDelta]cc[a_,b_]^q_:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]c[a_,b_]^q_:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_:> Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[x[\[Alpha]_],x[\[Beta]_]]:>{}/.\[CapitalDelta]f[x[\[Alpha]_],x[\[Beta]_]]:>{}/.\[CapitalDelta]c[x[\[Alpha]_],x[\[Beta]_]]:>{}/.\[CapitalDelta]f[x[\[Alpha]_],z[\[Beta]_]]:>{\[FilledSquare]<->z[\[Beta]]}/.\[CapitalDelta]f[z[\[Alpha]_],x[\[Beta]_]]:>{z[\[Alpha]]<->\[FilledSquare]}/.\[CapitalDelta]f[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}/.\[CapitalDelta]a[x[\[Alpha]_],z[\[Beta]_]]:>{\[FilledSquare]<->z[\[Beta]]}/.\[CapitalDelta]a[z[\[Alpha]_],x[\[Beta]_]]:>{z[\[Alpha]]<->\[FilledSquare]}/.\[CapitalDelta]a[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}/.\[CapitalDelta]c[x[\[Alpha]_],z[\[Beta]_]]:>{\[FilledSquare]<->z[\[Beta]]}/.\[CapitalDelta]c[z[\[Alpha]_],x[\[Beta]_]]:>{z[\[Alpha]]<->\[FilledSquare]}/.\[CapitalDelta]c[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}/.\[CapitalDelta]cc[z[\[Alpha]_],z[\[Beta]_]]:>{z[\[Alpha]]<->z[\[Beta]]}//Flatten},Which[pp==={},A,MemberQ[Module[{matr=Graph[pp]//IncidenceMatrix//Normal},Table[MemberQ[matr[[j]],1]&&MemberQ[matr[[j]],2]&&Plus@@matr[[j]]===4,{j,1,Length[matr]}]],True],0,True,Module[{test=NestWhile[Flatten[Map[SELFEN,#],1]&,SELFEN[pp/.x[\[Alpha]_]:>\[FilledSquare]],(FreeQ[#,"SELF"]&&Length[#]>0)& ]},Which[test==={},A,MemberQ[Flatten[{test}],"SELF"],0]]]]],A]
(* Check if one diagram contains non planar contribution (or if it is a pure no-planar contribution)
in= 1 Planar option activated
2 Planar option deactivated*)
planarity[p2_,s_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,in_]:=Which[in===1,p2/.Global`\[CapitalNu]^b_. a_.:> If[D[a,Global`\[CapitalMu]]===0,If[b===(s+m+3V1+3V2+3V3+4V4+4V5+6V6+3V7)/2-(V1+V2+V3+V4+V5+V6+V7)+1,Global`\[CapitalNu]^b a,0],Global`\[CapitalNu]^b a]/.Global`\[CapitalMu]^b_. a_.:> If[D[a,Global`\[CapitalNu]]===0,If[b===(s+m+3V1+3V2+3V3+4V4+4V5+6V6+3V7)/2-(V1+V2+V3+V4+V5+V6+V7)+1,Global`\[CapitalMu]^b a,0],Global`\[CapitalMu]^b a]/.Global`\[CapitalMu]^p_. Global`\[CapitalNu]^q_./;p+q!=(s+m+3V1+3V2+3V3+4V4+4V5+6V6+3V7)/2-(V1+V2+V3+V4+V5+V6+V7)+1:>0,in===2,p2]
(* ::Section::Closed:: *)
(*Contractions and Diagrams*)
(* Perform the wick contractions between fields *)
wick[list_]:=\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(ggg = 2\), \(Length[list]\)]\(\[LeftAngleBracket]list[\([1]\)], list[\([ggg]\)]\[RightAngleBracket]\ wick[Drop[Drop[list, {ggg}], 1]]\)\)
wick[{aaa_,bbb_}]:=\[LeftAngleBracket]aaa,bbb\[RightAngleBracket]
(* Merge the traces of the fields on the loop and the ones of the vertices in order to have only one trace at the end with the remaining fields to be contracted with wick *)
UnisciTracce[w_,tad_]:=Module[{w1=Plus@@((w/.a_\[CenterDot]b_:>If[b[[1]]==={},a\[CenterDot]Flatten[b],Table[(a\[LeftAngleBracket]b[[1,-1]],b[[qx+1,p]]\[RightAngleBracket])\[CenterDot]Flatten[{Drop[Drop[b,{1}],{qx}],{Flatten[Insert[Drop[b[[qx+1]],{p}],Drop[b[[1]],-1],p]]}},1],{qx,1,Length[b]-1},{p,1,Length[b[[qx+1]]]}]]/.rulesprop[tad]/.(0\[CenterDot]a_):>0)//Flatten)},If[Head[w1]===Plus,List@@w1,List@w1]]
Autocontraction[w_,tad_]:=Which[tad===2,w,tad===1,Module[{s=Plus@@(Flatten[{w/.a_\[CenterDot]b_:>Table[(a\[LeftAngleBracket]b[[1,-1]],b[[1,p]]\[RightAngleBracket])\[CenterDot]Flatten[{{Drop[Drop[b[[1]],{p}],{-1}]},Drop[b,{1}]},1],{p,1,Length[b[[1]]]-1}],w}]/.rulesprop[tad]/.(0\[CenterDot]a_):>0)},If[Head[s]=!=Plus,{s},List@@s]]]
UnicaTraccia[s_,n_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,tad_,UP_]:=Nest[UnisciTracce[Autocontraction[#,tad],tad]&,Nonvanishingtrace[s,n,m,V1,V2,V3,V4,V5,V6,V7,UP],V1+V2+V3+V4+V5+V6+V7]/.a_\[CenterDot]b_:>a\[CenterDot]Flatten[b]
(* substitution rules for the switch of two fields after the contraction *)
signrules:={aa_\[LeftAngleBracket]d[c__]\[CenterDot]Cb[a__],d[d1__]\[CenterDot]C[b__]\[RightAngleBracket]:>aa\[LeftAngleBracket]d[d1]\[CenterDot]C[b],d[c]\[CenterDot]Cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]r[c1__]\[CenterDot]cb[a__],d[d1__]\[CenterDot]c[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]d[d1]\[CenterDot]c[b],d[c1]\[CenterDot]cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]d[c1__]\[CenterDot]chb[a__],d[d1__]\[CenterDot]ch[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]d[d1]\[CenterDot]ch[b],d[c1]\[CenterDot]chb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]Cb[a__],d[c__]\[CenterDot]C[b__]\[RightAngleBracket]:>aa\[LeftAngleBracket]d[c]\[CenterDot]C[b],Cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]cb[a__],d[c1__]\[CenterDot]c[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]d[c1]\[CenterDot]c[b],cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]chb[a__],d[c1__]\[CenterDot]ch[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]d[c1]\[CenterDot]ch[b],chb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]d[c__]\[CenterDot]Cb[a__],C[b__]\[RightAngleBracket]:>aa\[LeftAngleBracket]C[b],d[c]\[CenterDot]Cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]d[c1__]\[CenterDot]cb[a__],c[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]c[b],d[c1]\[CenterDot]cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]d[c1__]\[CenterDot]chb[a__],ch[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]ch[b],d[c1]\[CenterDot]chb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]Cb[a__],C[b__]\[RightAngleBracket]:>aa\[LeftAngleBracket]C[b],Cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]cb[a__],c[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]c[b],cb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]chb[a__],ch[b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]ch[b],chb[a]\[RightAngleBracket],aa_\[LeftAngleBracket]\[Psi]b[a__],\[Psi][b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]\[Psi][b],\[Psi]b[a]\[RightAngleBracket],aa_\[LeftAngleBracket]\[CapitalPsi]b[a__],\[Psi][b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]\[Psi][b],\[CapitalPsi]b[a]\[RightAngleBracket],aa_\[LeftAngleBracket]\[CapitalPsi]b[a__],\[CapitalPsi][b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]\[CapitalPsi][b],\[CapitalPsi]b[a]\[RightAngleBracket],aa_\[LeftAngleBracket]\[Psi]b[a__],\[CapitalPsi][b__]\[RightAngleBracket]:>-aa\[LeftAngleBracket]\[CapitalPsi][b],\[Psi]b[a]\[RightAngleBracket]}
(* Perform the wick contractions, the Planar, Tadpoles and Self-energies checks and the relabelling of the indices *)
Contraction[s_,n_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,tad_,plan_,SE_,UP_]:=If[tad===2&&s===1,0,Module[{p4=relabelling\[Epsilon]\[Epsilon][relabelling\[Epsilon][relabelling\[Gamma][Module[{p3=Module[{p2=SEcheck[CountTadpole[Module[{p1=(Plus@@(Map[ReplaceAll[#,prop[\[Mu]]]&,UnicaTraccia[s,n,m,V1,V2,V3,V4,V5,V6,V7,tad,UP]/.a_ \[CenterDot] b_:>a wick[b]//.signrules/.rulesprop[tad]]//Expand))//.rule\[Delta]\[Delta]},With[{x=If[Head[p1]===Plus,List@@p1,List@p1],y=If[Head[p1]===Plus,(List@@p1/.Global`\[CapitalMu]:>1/.Global`\[CapitalNu]:>1),(List@p1/.Global`\[CapitalMu]:>1/.Global`\[CapitalNu]:>1)]},Plus@@(planarity[x/y,s,m,V1,V2,V3,V4,V5,V6,V7,plan]y)]],s,m,V1,V2,V3,V4,V5,V6,V7,tad],SE]},If[p2===0,Return[{}],If[Head[p2]===Times,{p2},List@@ p2]]]},With[{x=(p3/.\[Gamma][__][__]:>1/.\[Eta][__]:>1/.\[Eta]b[__]:>1)},(p3/x//.rule\[Eta]/.NonCommutativeMultiply[a___]:>CenterDot[a])x]/. CenterDot[Global`\[Eta][a___],b___,Global`\[Eta]b[c___]]:>((-1)^(Length[{b}]+1)) CenterDot[Global`\[Eta][a],b,Global`\[Eta]b[c]]]]]]},With[{x=(p4/.Global`nJ[__]:>1/.Global`nJb[__]:>1/.Global`M[__]:>1/.Global`Mh[__]:>1)},(p4/x//.ruleMn/.NonCommutativeMultiply[a___]:>CenterDot[a])x]]]/.CenterDot[a___][\[Alpha]_,\[Beta]_]:>RC[CenterDot[a]][\[Alpha],\[Beta]]
(* Draw the Feynman diagrams *)
grafici[y_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_]:=GraphPlot[Which[m===1,{(If[Head[y]===Times,List@@y,List@y]/.\[CapitalDelta]c[a_,b_]^q_.:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]cc[a_,b_]^q_.:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_.:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_.:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],1}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],2}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],4}/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],5},{{Global`\[LetterSpace]->x[\[Tau][1]],3}}}//Flatten[#,1]&,OddQ[m],{(If[Head[y]===Times,List@@y,List@y]/.\[CapitalDelta]c[a_,b_]^q_.:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]cc[a_,b_]^q_.:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_.:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_.:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],1}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],2}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],4}/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],5},Table[{x[\[Tau][i]]->x[\[Tau][i+1]],3},{i,1,m-1}]}//Flatten[#,1]&,True,{(If[Head[y]===Times,List@@y,List@y]/.\[CapitalDelta]c[a_,b_]^q_.:>Table[\[CapitalDelta]c[a,b],{u,1,q}]/.\[CapitalDelta]cc[a_,b_]^q_.:>Table[\[CapitalDelta]cc[a,b],{u,1,q}]/.\[CapitalDelta]a[a_,b_]^q_.:>Table[\[CapitalDelta]a[a,b],{u,1,q}]/.\[CapitalDelta]f[a_,b_]^q_.:>Table[\[CapitalDelta]f[a,b],{u,1,q}]//Flatten)/.\[CapitalDelta]a[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],1}/.\[CapitalDelta]f[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],2}/.\[CapitalDelta]c[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],4}/.\[CapitalDelta]cc[\[Alpha]_,\[Beta]_]:>{\[Alpha]->\[Beta],5},Table[{x[\[Tau][i]]->x[\[Tau][i+1]],3},{i,1,m/2-1}],Table[{x[\[Tau][i]]->x[\[Tau][i+1]],3},{i,m/2+1,m-1}],{{x[\[Tau][m/2]]->Global`\[LetterSpace],3},{x[\[Tau][m/2+1]]->Global`\[LetterSpace],3}}}//Flatten[#,1]&],EdgeRenderingFunction->(Switch[#3,1,{Darker[Green],Line[#1]},2,{Black,Line[#1]},3,{Red,Thick,Line[#1]},4,{Blue,Line[#1]},5,{Orange,Line[#1]}]&),VertexCoordinateRules->Which[m===1,Flatten[{Global`\[LetterSpace]->{0,0},x[\[Tau][1]]->{0.3,0},Table[z[k]->{1/8+1/8 Sin[k (2\[Pi])/(V1+V2+V3+V4+V5+V6+V7)+\[Pi]/2],1/10+1/8 Cos[k (2\[Pi])/(V1+V2+V3+V4+V5+V6+V7)+\[Pi]/2]},{k,1,V1+V2+V3+V4+V5+V6+V7}]}],OddQ[m],Flatten[{Table[x[\[Tau][k]]->{(m-(m-1)/2-k),Abs[m-(m-1)/2-k]Sin[\[Pi]/2 Abs[m-(m-1)/2-k] 1/m]},{k,1,m}],Table[z[k]->{1/4 Sin[k (2\[Pi])/(V1+V2+V3+V4+V5+V6+V7)+\[Pi]/4],(m-1)/5+1/4 Cos[k (2\[Pi])/(V1+V2+V3+V4+V5+V6+V7)+\[Pi]/4]},{k,1,V1+V2+V3+V4+V5+V6+V7}]}],EvenQ[m],Flatten[{Table[x[\[Tau][k]]->{m-(m-2)/2-k,Abs[m-(m-2)/2-k]Sin[\[Pi]/2 Abs[m-(m-1)/2-k] 1/m]},{k,1,m/2}],Global`\[LetterSpace]->{0,0},Table[x[\[Tau][k]]->{(m/2-k),Abs[m/2-k]Sin[\[Pi]/2 Abs[m-(m-1)/2-k] 1/m]},{k,m/2+1,m}],Table[z[k]->{1/4 Sin[k (2\[Pi])/(V1+V2+V3+V4+V5+V6+V7)+\[Pi]/4],(m+1)/5+1/4 Cos[k (2\[Pi])/(V1+V2+V3+V4+V5+V6+V7)+\[Pi]/4]},{k,1,V1+V2+V3+V4+V5+V6+V7}]}]],VertexLabeling->True,VertexRenderingFunction->({White,EdgeForm[Black],Disk[#,.05 Which[m===1,.25,m===2,1,True,m/2]],Black,Text[#2,#1]}&),ImageSize->450]/.x[\[Tau][a_]]:>a/.z[a_]:>a
(* Use the Contraction and grafici functions putting togheter different integrands with the same diagram.
If the input data are not valid it will show an error message*)
Diagrammi[s_,n_,m_,V1_,V2_,V3_,V4_,V5_,V6_,V7_,tad_,plan_,SE_,UP_]:=(Which[n<0||m<0||s-n-m<0||V1<0||V2<0||V3<0||V4<0||V5<0||V6<0||V7<0||!IntegerQ[n]||!IntegerQ[m]||!IntegerQ[s-m-n]||!IntegerQ[V1]||!IntegerQ[V2]||!IntegerQ[V3]||!IntegerQ[V4]||!IntegerQ[V5]||!IntegerQ[V6]||!IntegerQ[V7],StringJoin@@{"\!\(\*
StyleBox[\"INVALID\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"DATA\",\nFontColor->RGBColor[1, 0, 0]]\)",": The number of fields on the Wilson loop and the number of the vertices must be 0 or a positive integer"},s===0,If[V1===0&&V2===0&&V3===0&&V4===0&&V5===0&&V6===0&&V7===0,If[UP===1,Global`\[CapitalNu],Global`\[CapitalMu]],StringJoin@@{"\!\(\*
StyleBox[\"NOT\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"-\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"CONNECTED\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"DIAGRAMS\",\nFontColor->RGBColor[1, 0, 0]]\)",": The number of fields on the Wilson loop must be larger than 0 if the total number of vertices is larger than 0"}],OddQ[V1+n+3V2+V3+2V4+V7],StringJoin@@{"\!\(\*
StyleBox[\"ODD\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"NUMBER\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"OF\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"GAUGE\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"FIELDS\",\nFontColor->RGBColor[1, 0, 0]]\)",": Try to modify the number of gauge fields on the Wilson loop or the number of vertices V1, V2, V3, V4 or V7"},OddQ[s-n-m+2V1+2V5],StringJoin@@{"\!\(\*
StyleBox[\"ODD\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"NUMBER\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"OF\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"FERMION\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"FIELDS\",\nFontColor->RGBColor[1, 0, 0]]\)",": Try to modify the number of fermion fields on the Wilson loop or the number of vertices V1 or V5"},True,Module[{b1=Contraction[s,n,m,V1,V2,V3,V4,V5,V6,V7,tad,plan,SE,UP]},Which[b1==={},{},b1===0,{},True,Module[{p1=((b1//.CenterDot[a___]:>Times[a])/(b1//.CenterDot[a___]:>Times[a]/.\[CapitalDelta]a[a_,b_]:>1/.\[CapitalDelta]cc[a_,b_]:>1/.\[CapitalDelta]c[a_,b_]:>1/.\[CapitalDelta]f[a_,b_]:>1))/.\[CapitalDelta]f[a___]:>\[CapitalDelta]f[Sequence@@Sort[List@a]]/.\[CapitalDelta]f[x[\[Alpha]_],z[\[Beta]_]]:>\[CapitalDelta]f[z[\[Beta]],x[\[Alpha]]]/.\[CapitalDelta]a[a___]:>\[CapitalDelta]a[Sequence@@Sort[List@a]]/.\[CapitalDelta]a[x[\[Alpha]_],z[\[Beta]_]]:>\[CapitalDelta]a[z[\[Beta]],x[\[Alpha]]]/.\[CapitalDelta]c[a___]:>\[CapitalDelta]c[Sequence@@Sort[List@a]]/.\[CapitalDelta]c[x[\[Alpha]_],z[\[Beta]_]]:>\[CapitalDelta]c[z[\[Beta]],x[\[Alpha]]]/.\[CapitalDelta]cc[a___]:>\[CapitalDelta]cc[Sequence@@Sort[List@a]]},Module[{p2=Module[{w=((Plus@@p1)/.a_ b_/;a\[Element]Integers:>b)},If[Head[w]===Plus,List@@w,{w}]]},Table[{grafici[p2[[j]],s,V1,V2,V3,V4,V5,V6,V7],Plus@@(b1[[#]]&@Flatten[Position[p1,p2[[j]]]])},{j,1,Length[p2]}]]]]]]//Quiet)/.\[CapitalDelta]a[a___]:>Global`\[CapitalDelta][a]/.\[CapitalDelta]c[a___]:>Global`\[CapitalDelta][a]/.\[CapitalDelta]cc[a___]:>Global`\[CapitalDelta][a]/.\[CapitalDelta]f[a___]:>Global`\[CapitalDelta][a]/.d[a___]:>Global`d[a]/.z[a___]:>Global`z[a]/.x[a___]:>Global`x[a]/.\[Tau][a___]:>Global`\[Tau][a]/.xp[a___]:>Global`xp[a]/.CenterDot[Global`M[Global`\[Tau][a_]],b___,Global`M[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`M[Global`\[Tau][a]],b,Global`M[Global`\[Tau][c]]]]//.A_ Global`M[Global`\[Tau][a_]]:>A Global`tr[Global`M[Global`\[Tau][a]]]/.CenterDot[Global`\[Gamma][a_],b___,Global`\[Gamma][c_]]:>Global`tr[CenterDot[Global`\[Gamma][a],b,Global`\[Gamma][c]]]//.A_ Global`\[Gamma][a_]:>A Global`tr[Global`\[Gamma][a]]/.Global`d[a_,b_]\[CenterDot]A_:>Global`d[a,b,A]/.Global`d[a_,b_]\[CenterDot]Global`d[c_,d1_]\[CenterDot]A_:>Global`d[a,b,Global`d[c,d1,A]]/.CenterDot[Global`Mh[Global`\[Tau][a_]],b___,Global`Mh[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`Mh[Global`\[Tau][a]],b,Global`Mh[Global`\[Tau][c]]]]//.A_ Global`Mh[Global`\[Tau][a_]]:>A Global`tr[Global`Mh[Global`\[Tau][a]]]/.CenterDot[Global`Mh[Global`\[Tau][a_]],b___,Global`M[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`Mh[Global`\[Tau][a]],b,Global`M[Global`\[Tau][c]]]]/.CenterDot[Global`M[Global`\[Tau][a_]],b___,Global`Mh[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`M[Global`\[Tau][a]],b,Global`Mh[Global`\[Tau][c]]]]
(* Compute all the possible input data of Diagrammi for a chosen perturbative order *)
fullorder[p_,tad_,plan_,SE_,UP_]:=Which[p<0||!IntegerQ[p],StringJoin@@{"\!\(\*
StyleBox[\"INVALID\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"DATA\",\nFontColor->RGBColor[1, 0, 0]]\)",": The perturbative order must be 0 or a positive integer"},p===0,{{0,0,0,0,0,0,0,0,0,0,tad,plan,SE,UP}},True,Module[{gg=Module[{s=Module[{q=(Table[{f,n,m,V1,V2,V3,V4,V5,V6,V7,(f+n+2m+3V1+3V2+3V3+4V4+4V5+6V6+7V7)/2-(V1+V2+V3+V4+V5+V6+V7)},{f,0,2p},{n,0,2p},{m,0,p},{V1,0,If[tad===1,p,2p-1]},{V2,0,If[tad===1,p-V1,2p-V1-1]},{V3,0,If[tad===1,p-V1-V2,2p-V1-V2-1]},{V4,0,If[tad===1,p-V1-V2-V3,2p-V1-V2-V3-1]},{V5,0,If[tad===1,p-V1-V2-V3-V4,2p-V1-V2-V3-V4-1]},{V6,0,If[tad===1,p-V1-V2-V3-V4-V5,2p-V1-V2-V3-V4-V5-1]},{V7,0,If[tad===1,p-V1-V2-V3-V4-V5-V6,2p-V1-V2-V3-V4-V5-V6-1]}]//Flatten[#,9]&)},q[[#]]&@Flatten[Position[q,{__,p}]]]/.{a_,b_,c_,d_,e_,f_,g_,h_,h1_,h2_, i_}:>{a+b+c,b,c,d,e,f,g,h,h1,h2,tad,plan,SE,UP}},Drop[s,Flatten[{1,FirstPosition[s,{1,__}]-1}]]]},Delete[gg,Position[gg/.{a_,b_,c_,d_,e_,f_,g_,h_,h1_,h2_, i_,j_,k_,UP1_}/;OddQ[d+b+3e+f+2g+h2]||OddQ[a-b-c+2d+2h]||Which[tad===2,a===1,tad===1,False]:>"zero","zero"]]]]
(* ::Section::Closed:: *)
(*Package Functions*)
(* main functions of the package (see the manual) *)
WiLE=Interpretation[{f=0,n=0,m=0,V1=0,V2=0,V3=0,V4=0,V5=0,V6=0,V7=0,tad=2,plan=1,SE=2,UP=1},Panel[Grid[{{Style["WiLE",Bold],SpanFromLeft},{},{"Supermatrix Sector",RadioButtonBar[Dynamic[UP],{1->"UL",2->"LD"}]},{},{"# of fermion fields on the loop:",InputField[Dynamic[f]]},{"# of gauge fields on the loop:",InputField[Dynamic[n]]},{"# of scalar fields on the loop:",InputField[Dynamic[m]]},{},{"# of vertices A\[Psi]\[Psi]:",InputField[Dynamic[V1]]},{"# of vertices AAA:",InputField[Dynamic[V2]]},{"# of vertices ACC:",InputField[Dynamic[V3]]},{"# of vertices AACC:",InputField[Dynamic[V4]]},{"# of vertices CC\[Psi]\[Psi]:",InputField[Dynamic[V5]]},{"# of vertices CCCCCC:",InputField[Dynamic[V6]]},{"# of vertices Acc:",InputField[Dynamic[V7]]},{},{"Planar",RadioButtonBar[Dynamic[plan],{1->"on",2->"off"}]},{"Tadpoles",RadioButtonBar[Dynamic[tad],{1->"on",2->"off"}]},{"Self-Energies",RadioButtonBar[Dynamic[SE],{1->"on",2->"off"}]},{},{"Perturbative Order:",Dynamic[With[{ord=(f+n+2m+3V1+3V2+3V3+4V4+4V5+6V6+3V7)/2-(V1+V2+V3+V4+V5+V6+V7)},If[IntegerQ[ord],ord,"\[NotElement] Integers"]]]}}]],(Diagrammi[f+n+m,n,m,V1,V2,V3,V4,V5,V6,V7,tad,plan,SE,UP])];
WiLEFullorder=Interpretation[{n=0,tad=2,plan=1,SE=2,UP=1},Panel[Grid[{{Style["WiLEFullorder",Bold],SpanFromLeft},{},{"Supermatrix Sector",RadioButtonBar[Dynamic[UP],{1->"UL",2->"LD"}]},{},{"Perturbative order:",InputField[Dynamic[n]]},{},{"Planar",RadioButtonBar[Dynamic[plan],{1->"on",2->"off"}]},{"Tadpoles",RadioButtonBar[Dynamic[tad],{1->"on",2->"off"}]},{"Self-Energies",RadioButtonBar[Dynamic[SE],{1->"on",2->"off"}]}}]],Module[{full=fullorder[n,tad,plan,SE,UP]},If[Head[full]===String,full,(Diagrammi@@@full)//Flatten[#,1]&]]/.{Global`\[CapitalMu]}->Global`\[CapitalMu]/.{Global`\[CapitalNu]}->Global`\[CapitalNu]];
WiLESimplify[A_]:=((((A//.Global`\[Epsilon]\[Epsilon][a_,b_,c_,d_]Global`\[Epsilon]\[Epsilon][i_,j_,k_,l_]/;a===i||a===j||a===k||a===l||b===i||b===j||b===k||b===l||c===i||c===j||c===k||c===l||d===i||d===j||d===k||d===l:>\[Delta]\[Delta]1[a,l] \[Delta]\[Delta]1[b,k] \[Delta]\[Delta]1[c,j] \[Delta]\[Delta]1[d,i]-\[Delta]\[Delta]1[a,k] \[Delta]\[Delta]1[b,l] \[Delta]\[Delta]1[c,j] \[Delta]\[Delta]1[d,i]-\[Delta]\[Delta]1[a,l] \[Delta]\[Delta]1[b,j] \[Delta]\[Delta]1[c,k] \[Delta]\[Delta]1[d,i]+\[Delta]\[Delta]1[a,j] \[Delta]\[Delta]1[b,l] \[Delta]\[Delta]1[c,k] \[Delta]\[Delta]1[d,i]+\[Delta]\[Delta]1[a,k] \[Delta]\[Delta]1[b,j] \[Delta]\[Delta]1[c,l] \[Delta]\[Delta]1[d,i]-\[Delta]\[Delta]1[a,j] \[Delta]\[Delta]1[b,k] \[Delta]\[Delta]1[c,l] \[Delta]\[Delta]1[d,i]-\[Delta]\[Delta]1[a,l] \[Delta]\[Delta]1[b,k] \[Delta]\[Delta]1[c,i] \[Delta]\[Delta]1[d,j]+\[Delta]\[Delta]1[a,k] \[Delta]\[Delta]1[b,l] \[Delta]\[Delta]1[c,i] \[Delta]\[Delta]1[d,j]+\[Delta]\[Delta]1[a,l] \[Delta]\[Delta]1[b,i] \[Delta]\[Delta]1[c,k] \[Delta]\[Delta]1[d,j]-\[Delta]\[Delta]1[a,i] \[Delta]\[Delta]1[b,l] \[Delta]\[Delta]1[c,k] \[Delta]\[Delta]1[d,j]-\[Delta]\[Delta]1[a,k] \[Delta]\[Delta]1[b,i] \[Delta]\[Delta]1[c,l] \[Delta]\[Delta]1[d,j]+\[Delta]\[Delta]1[a,i] \[Delta]\[Delta]1[b,k] \[Delta]\[Delta]1[c,l] \[Delta]\[Delta]1[d,j]+\[Delta]\[Delta]1[a,l] \[Delta]\[Delta]1[b,j] \[Delta]\[Delta]1[c,i] \[Delta]\[Delta]1[d,k]-\[Delta]\[Delta]1[a,j] \[Delta]\[Delta]1[b,l] \[Delta]\[Delta]1[c,i] \[Delta]\[Delta]1[d,k]-\[Delta]\[Delta]1[a,l] \[Delta]\[Delta]1[b,i] \[Delta]\[Delta]1[c,j] \[Delta]\[Delta]1[d,k]+\[Delta]\[Delta]1[a,i] \[Delta]\[Delta]1[b,l] \[Delta]\[Delta]1[c,j] \[Delta]\[Delta]1[d,k]+\[Delta]\[Delta]1[a,j] \[Delta]\[Delta]1[b,i] \[Delta]\[Delta]1[c,l] \[Delta]\[Delta]1[d,k]-\[Delta]\[Delta]1[a,i] \[Delta]\[Delta]1[b,j] \[Delta]\[Delta]1[c,l] \[Delta]\[Delta]1[d,k]-\[Delta]\[Delta]1[a,k] \[Delta]\[Delta]1[b,j] \[Delta]\[Delta]1[c,i] \[Delta]\[Delta]1[d,l]+\[Delta]\[Delta]1[a,j] \[Delta]\[Delta]1[b,k] \[Delta]\[Delta]1[c,i] \[Delta]\[Delta]1[d,l]+\[Delta]\[Delta]1[a,k] \[Delta]\[Delta]1[b,i] \[Delta]\[Delta]1[c,j] \[Delta]\[Delta]1[d,l]-\[Delta]\[Delta]1[a,i] \[Delta]\[Delta]1[b,k] \[Delta]\[Delta]1[c,j] \[Delta]\[Delta]1[d,l]-\[Delta]\[Delta]1[a,j] \[Delta]\[Delta]1[b,i] \[Delta]\[Delta]1[c,k] \[Delta]\[Delta]1[d,l]+\[Delta]\[Delta]1[a,i] \[Delta]\[Delta]1[b,j] \[Delta]\[Delta]1[c,k] \[Delta]\[Delta]1[d,l]//.Global`\[Epsilon][a_,b_,c_]Global`\[Epsilon][i_,j_,k_]/;a===i||a===j||a===k||b===i||b===j||b===k||c===i||c===j||c===k:>(-\[Delta]\[Delta][a,k] \[Delta]\[Delta][b,j] \[Delta]\[Delta][c,i]+\[Delta]\[Delta][a,j] \[Delta]\[Delta][b,k] \[Delta]\[Delta][c,i]+\[Delta]\[Delta][a,k] \[Delta]\[Delta][b,i] \[Delta]\[Delta][c,j]-\[Delta]\[Delta][a,i] \[Delta]\[Delta][b,k] \[Delta]\[Delta][c,j]-\[Delta]\[Delta][a,j] \[Delta]\[Delta][b,i] \[Delta]\[Delta][c,k]+\[Delta]\[Delta][a,i] \[Delta]\[Delta][b,j] \[Delta]\[Delta][c,k])//Expand)//.{\[Delta]\[Delta]1[a_,b_]\[Delta]\[Delta]1[b_,c_]:>\[Delta]\[Delta]1[a,c],\[Delta]\[Delta]1[a_,b_]^2:>4,\[Delta]\[Delta]1[a_,b_]Global`nJ[Global`\[Tau][c_],b_]:>Global`nJ[Global`\[Tau][c],a],\[Delta]\[Delta]1[a_,b_]Global`nJb[Global`\[Tau][c_],b_]:>Global`nJb[Global`\[Tau][c],a],\[Delta]\[Delta]1[a_,a_]:>4,\[Delta]\[Delta]1[a_,b_]c_:>(c/.a->b),\[Delta]\[Delta][a_,b_]\[Delta]\[Delta][b_,c_]:>\[Delta]\[Delta][a,c],\[Delta]\[Delta][a_,b_]^2:>3,\[Delta]\[Delta][a_,a_]:>3,\[Delta]\[Delta][a_,b_]c_:>(c/.a->b)}//.ruleMn/.NonCommutativeMultiply[a___]:>CenterDot[a])/.Global`\[Epsilon][a_,b_,c_]/;a===b||a===c||c===b:>0/.Global`\[Epsilon]\[Epsilon][a_,b_,c_,d_]/;a===b||a===c||a===d||c===b||c===d||b===d:>0)//.AA_ Global`xp[Global`\[Tau][a_],Global`\[Mu][b_]]:>(AA/.Global`\[Mu][b]->Global`\[Nu][a])Global`xp[Global`\[Tau][a],Global`\[Nu][a]]/.Global`\[CapitalDelta][a_,b_]:>Sort[Global`\[CapitalDelta][a,b]]//.AA_. Global`d[b_,\[Mu]_,Global`\[CapitalDelta][a_,b_]]/;a=!=b:>-AA Global`d[a,\[Mu],Global`\[CapitalDelta][a,b]]/.Global`\[Epsilon][aa_,b_,c_]:>Signature[{aa,b,c}]Sort[Global`\[Epsilon][aa,b,c]]//Simplify)/.CenterDot[Global`M[Global`\[Tau][a_]],b___,Global`M[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`M[Global`\[Tau][a]],b,Global`M[Global`\[Tau][c]]]]//.AAA_ Global`M[Global`\[Tau][a_]]:>AAA Global`tr[Global`M[Global`\[Tau][a]]]/.CenterDot[Global`Mh[Global`\[Tau][a_]],b___,Global`Mh[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`Mh[Global`\[Tau][a]],b,Global`Mh[Global`\[Tau][c]]]]//.AAA_ Global`Mh[Global`\[Tau][a_]]:>AAA Global`tr[Global`Mh[Global`\[Tau][a]]]/.CenterDot[Global`Mh[Global`\[Tau][a_]],b___,Global`M[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`Mh[Global`\[Tau][a]],b,Global`M[Global`\[Tau][c]]]]/.CenterDot[Global`M[Global`\[Tau][a_]],b___,Global`Mh[Global`\[Tau][c_]]]:>Global`tr[CenterDot[Global`M[Global`\[Tau][a]],b,Global`Mh[Global`\[Tau][c]]]]
End[]
EndPackage[]