Bound-electron self-energy calculations in Feynman and Coulomb gauges: detailed analysis

TL;DR

This paper compares the convergence of partial-wave-expansion methods for calculating the self-energy correction in the Lamb shift within Feynman and Coulomb gauges, offering insights to improve computational accuracy.

Contribution

It provides a detailed comparative analysis of gauge-dependent convergence issues and discusses techniques to enhance the accuracy of self-energy calculations in quantum electrodynamics.

Findings

Feynman gauge shows different convergence behavior than Coulomb gauge.

Certain tricks can improve the partial-wave-expansion convergence.

The analysis aids in refining self-energy correction calculations.

Abstract

The energy correction associated with the self-energy diagram is the leading (in magnitude) and fundamental (in significance) contribution to the Lamb shift in highly charged ions. Conventional approaches to this correction rely on partial-wave expansions, which is a stumbling block limiting accuracy. To elucidate the issue, we perform a comprehensive comparative analysis of partial-wave-expansion convergence between two gauges: Feynman and Coulomb. Some tricks for improving the convergence are discussed as well.