Infrared divergences, mass shell singularities and gauge dependence of the dynamical fermion mass

TL;DR

This paper investigates how infrared divergences and gauge choices affect the dynamical fermion mass in gauge theories, showing gauge dependence in covariant gauges and gauge independence in physical gauges at one loop.

Contribution

It demonstrates that in the massive Schwinger model, the fermion mass's gauge dependence and divergences are resolved in physical gauges at one loop, contrasting with covariant gauges.

Findings

Fermion propagator pole is divergent and gauge dependent in covariant gauges at one loop.

Leading singularities cancel in the quenched rainbow approximation.

Dynamical fermion mass is finite and gauge independent in physical gauges at one loop.

Abstract

We study the behavior of the dynamical fermion mass when infrared divergences and mass shell singularities are present in a gauge theory. In particular, in the massive Schwinger model in covariant gauges we find that the pole of the fermion propagator is divergent and gauge dependent at one loop, but the leading singularities cancel in the quenched rainbow approximation. On the other hand, in physical gauges, we find that the dynamical fermion mass is finite and gauge independent at least up to one loop.