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in first quantization, we develop an effective QED Hamiltonian in a fermionic Fock-space. This effective QED theory includes the effects of the vacuum polarization but does not include the photon degrees of freedom [5,6,7]. Within this framework we are able to calculate the vacuum-polarization density and the QED Lamb-type shift of the bound-state energy.


[^1] P. Pyykkö, Annu. Rev. Phys. Chem. 63, 45 (2012).
[^2] D.Traore, E.Giner and J. Toulouse, J. Chem. Phys. 156, 044113 (2022).
[^3] T.Audinet and J.Toulouse, J. Chem. Phys. 158, 244108 (2023).
[^4] I.R.Lapidus, Am. J. Phys. 51, 1036 (1983).
[^5] P. Chaix and D. Iracane, J. Phys. B 22, 3791 (1989).
[^6] C. Hainzl, M. Lewin, E. Séré and J. P. Solovej, Phys. Rev. A 76, 052104 (2007).
[^7] J. Toulouse, SciPost Chem. 1, 2 (2021).
[^1]: P. Pyykkö, Annu. Rev. Phys. Chem. 63, 45 (2012).
[^2]: D.Traore, E.Giner and J. Toulouse, J. Chem. Phys. 156, 044113 (2022).
[^3]: T.Audinet and J.Toulouse, J. Chem. Phys. 158, 244108 (2023).
[^4]: I.R.Lapidus, Am. J. Phys. 51, 1036 (1983).
[^5]: P. Chaix and D. Iracane, J. Phys. B 22, 3791 (1989).
[^6]: C. Hainzl, M. Lewin, E. Séré and J. P. Solovej, Phys. Rev. A 76, 052104 (2007).
[^7]: J. Toulouse, SciPost Chem. 1, 2 (2021).

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