The pole of the fermion propagator in a general class of gauges

TL;DR

This paper investigates how the pole of the fermion propagator in QED behaves across various gauges, demonstrating gauge independence of the fermion mass under certain conditions using Nielsen identities.

Contribution

It introduces a method to analyze gauge dependence of the fermion propagator pole in a broad class of gauges using Nielsen identities, valid to all orders in perturbation theory.

Findings

Fermion pole mass is gauge independent in the absence of infrared divergences.

Nielsen identities relate gauge variations to the fermion two-point function.

The analysis applies to a general class of gauges interpolating between known gauge choices.

Abstract

We study the behavior of the pole of the fermion propagator, in QED in $n$-dimensions, in a general class of gauges which interpolate between the covariant, the axial and the Coulomb gauges. We use Nielsen identities, following from the BRST invariance of the theory, to determine the gauge variation of the fermion two point function in this general class of gauges. This allows us to show directly and in a simple manner, to all orders in perturbation theory, that in the absence of infrared divergences and mass shell singularities, the fermion pole mass is gauge independent.