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This is a repo for dumping notes & homework, released under CC-BY-NC-SA 4.0.

PDF is usually compiled using xelatex & biber. However, if there are Feynman diagrams created with tikz-feynman, then it should be compiled with lualatex. The LaTeX engine to use is specified with a magic comment, e.g.

% !TeX TS-program = lualatex

For PDFs, please go to Releases; they are also hosted on:

PDFs are generated by Github actions & workflows; for implementations, see .github/.

Strings2020 strings

String Theory, Spring 2020, by Prof. Chi-Ming Chang @ Tsinghua.

Contents:

  1. Classical spinning string, conformal transformations, bc CFT & Noether's theorem, SO(n) free fermion CFT and current algebra;
  2. BRST current of bosonic string, detailed calculations of OPE, normal ordering ambiguity, linear dilaton CFT, bosonic strings on S^3 & Dirac's quantization, and anomalous current from curvature;
  3. Perturbative calculation of beta functions, classical 11D gravity & Freund–Robin compactification, SUSY counting with Killing spinors, superspace formalism, and mixed diffeo-axial anomaly in standard model;
  4. Vertex operators, contraction of exponentials, symmetry of 3-point functions, D0-string scattering calculated with CKV & image charge, and gluon-tachyon scattering;
  5. Compact scalar with winding, zero point fixing, partition function and modular invariance, orbifold & twisted sectors, torus bc path integral, and torus propagator as a trace;
  6. Type 0 superstring from consistency conditions, GSO projections & partition functions, KK mechanism & 5D theory, fiberwise T-duality from path integral, dilaton shift, cylinder diagram factorization & only one coupling in string theory;
  7. T-duality of heterotic strings, Wilson line background & symmetry breaking, string junctions & SUSY counting, 2-pt / 3-pt functions in AdS/CFT from boundary-to-bulk propagators and conformal symmetry.

AdvancedQFT2020 advqft

Advanced Quantum Field Theory, Spring 2020, by Prof. Wenbin Yan & Prof. Dan Xie @ Tsinghua.

Contents:

  1. Noether's theorem & Poincare algebra;
  2. Finite gauge transformation & Chern-Simons form, Faddeev-Popov quantization for particles & strings;
  3. BRST transformation in Yang-Mills theory, and BRST quantization of point particle.

gauge

A non-technical note on the geometry of gauge theory, including bundles and connection, with discussions about tetrad formalism and spin connection in gravity.

ThermalFieldTheory2020 thermal

Finite Temperature Field Theory, Spring 2020, by Prof. Lian-Yi He @ Tsinghua

Contents:

  1. Thermal propagator of free theory, from path integral;
  2. Pure QED partition function in covariant gauge, with Faddeev-Popov quantization & mode expansions;
  3. QCD partition function from Feynman diagrams, with tricks to compute Matsubara sums;
  4. Ward identity with hard thermal loop (HTL), decomposition of transverse self-energy using projections, and HTL in QCD;
  5. Correlations of Pauli spinors, using effective formalism & perturbative expansions, with full calculations of Matsubara sums & frequency integral; results expressed in spectral functions.

SpinorGR spinor

An intuitive introduction of spin structure & spinor in general relativity (GR), with discussions of physical motivations, and a sketch of Witten's proof of the positive energy theorem. Written as the final paper for Differential Geometry, a course in Fall 2019 given by Prof. Hui Ma @ Tsinghua.

AlgebraicTopology2020 algtop

Algebraic Topology, Spring 2020, by Prof. Si Li @ Tsinghua

Incomplete due to early withdrawn, but contains some nice commutative diagrams.