Abstract
(See, for instance, Mandl and Shaw [(Måartensson J Phys B 12:3995–4012, 1980, [143]), Chap. 9] and Peskin and Schroeder [Pople et al. Int J Quantum Chem 14:545–60, 1978, [194], Chap. 7].)
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Notes
- 1.
In the following we shall for simplicity denote the electron physical mass by m instead of \(m_e\).
- 2.
Here, \(S_{\mathrm{{F}}}^\mathrm{{free}}(p)\) is the non-covariant electron propagator, defined by means of \(\varPsi ^{\dag }\) in the formulas (4.9), while \(\overline{S_{\mathrm{{F}}}}^\mathrm{{free}}(p)\) is the corresponding covariant expression, defined by means of \({\bar{\varPsi }}=\varPsi ^{\dag }\beta \).
- 3.
Note that \(\varSigma (\omega ,\varvec{\mathrm{{p}}})\) has the dimension of energy and that the product \(\varSigma (\omega ,\varvec{\mathrm{{p}}})\,S_{\mathrm{{F}}}(\omega ,\varvec{\mathrm{{p}}})\) is dimensionfree (see Appendix K).
- 4.
We use the convention that \(\mu ,\,\nu ,\ldots \) represent all four components (0,1,2,3), while \(i,\,j,\ldots \) represent the vector part (1,2,3).
- 5.$$ \int _0^1\mathrm {d}x\int _0^1\mathrm {d}y\,\sqrt{y}\;\ln (xy)=-\frac{10}{9}\,;\quad \int _0^1\mathrm {d}x\,x\int _0^1\mathrm {d}y\,\sqrt{y}\;\ln (xy)=-\frac{1}{18}\,; $$$$ \int _0^1\mathrm {d}x\,x\int _0^1\mathrm {d}y\,y\sqrt{y}\;\ln (xy)=-\frac{9}{50} $$
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Lindgren, I. (2016). Regularization and Renormalization. In: Relativistic Many-Body Theory. Springer Series on Atomic, Optical, and Plasma Physics, vol 63. Springer, Cham. https://doi.org/10.1007/978-3-319-15386-5_12
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DOI: https://doi.org/10.1007/978-3-319-15386-5_12
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