One loop Volkov propagator in the Lorentz class of gauges

TL;DR

This paper calculates ultraviolet divergences in the Volkov propagator across all Lorentz gauges, revealing gauge-dependent renormalization effects and the unique divergence removal in Landau gauge.

Contribution

It provides the first comprehensive analysis of ultraviolet divergences in the Volkov propagator within the full Lorentz gauge class, highlighting gauge dependence of mass shift renormalization.

Findings

Vacuum mass shift gauge invariance is confirmed.

Renormalization of the mass shift depends on the gauge choice.

Ultraviolet divergences are only fully removed in Landau gauge.

Abstract

We calculate the ultraviolet divergences in a weak field expansion of the Volkov propagator. This is done for the full Lorentz class of gauges. The expected gauge invariance of the vacuum mass shift in each sideband is recovered. However, the renormalisation of the background induced mass shift is shown to be gauge dependent. In particular, we show that it vanishes in Landau gauge. We find that only in that gauge does the vacuum renormalisation remove all ultraviolet divergences.