Dimensional regularization of the free-electron self-energy and vertex correction in Coulomb gauge

TL;DR

This paper verifies and derives formulas for the free-electron self-energy and vertex correction in Coulomb gauge, facilitating more accurate quantum electrodynamics calculations for highly charged ions.

Contribution

It provides detailed derivations and validation of Adkins' formulas for self-energy and vertex corrections in Coulomb gauge, enhancing computational methods in QED.

Findings

Formulas for electron self-energy and vertex correction are verified.

Derivations of these formulas are provided in detail.

Results support improved accuracy in QED calculations for ions.

Abstract

There is presently a great interest in studying static and dynamic properties of highly charged ions that can be produced in large particle accelerators, like that at GSI in Darmstadt. To perform corresponding theoretical calculations with great accuracy requires a highly developed machinery of computational methods that have not until recently been available. In order to combine many-body perturbation theory with quantum electrodynamics, the calculations have generally to be performed in the Coulomb gauge, where applications have not been so developed as in, for instance, the Feynman gauge. Formulas for the free-electron self energy and vertex correction have been given without derivation by Adkins (Phys. Rev. D27, 1814 (1983); Phys. Rev. D34, 2489 (1986)). In the present paper the formulas of Adkins are verified with detailed derivations.