Abstract
(See, for instance, Mandl and Shaw [17, Chap. 9] and Peskin and Schroeder [23, 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.
The factor of β appears here because we define the electron propagator (4.9) by means of \({\hat{\psi }}^{\dag }\) instead of the more conventionally used \(\bar{\hat{\psi }} ={ \hat{\psi }}^{\dag }\beta \).
- 3.
Note that Σ(ω, p) has the dimension of energy and that the product Σ(ω, p) SF(ω, p) is dimensionless (see Appendix K).
- 4.
We use the convention that μ, ν, … represent all four components (0,1,2,3), while i, j, … represent the vector part (1,2,3).
- 5.$${\int \nolimits \nolimits }_{0}^{1}\mathrm{d}x{\int \nolimits \nolimits }_{0}^{1}\mathrm{d}y\,\sqrt{y}\;\ln (xy) = -\frac{10} {9} \,; \quad { \int \nolimits \nolimits }_{0}^{1}\mathrm{d}x\,x{\int \nolimits \nolimits }_{0}^{1}\mathrm{d}y\,\sqrt{y}\;\ln (xy) = - \frac{1} {18}\,;$$$${\int \nolimits \nolimits }_{0}^{1}\mathrm{d}x\,x{\int \nolimits \nolimits }_{0}^{1}\mathrm{d}y\,y\sqrt{y}\;\ln (xy) = - \frac{9} {50}.$$
- 6.
A complete treatment of the vertex correction is being published separately in arXiv:quant-ph.
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Lindgren, I. (2011). Regularization and Renormalization. In: Relativistic Many-Body Theory. Springer Series on Atomic, Optical, and Plasma Physics, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8309-1_12
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