Curing Fermion Mass Gauge Variance in QED$_{2+1}$

TL;DR

This paper demonstrates that the fermion mass shell in Maxwell-Chern-Simons QED in 2+1 dimensions remains gauge-invariant at all perturbation orders by employing a Proca mass term as an infrared regulator.

Contribution

It introduces a method using a Proca mass term to prove gauge invariance of the fermion mass shell in QED$_{2+1}$ across all perturbation orders.

Findings

Fermion mass shell is gauge-invariant in QED$_{2+1}$.

Proca mass term effectively regulates infrared divergences.

Gauge dependence issues are resolved at all perturbation levels.

Abstract

The problem of the gauge dependence of the fermion mass in the Maxwell-Chern-Simons QED$_{2+1}$ is revisited. Using Proca mass term as an intermediate infrared regulator we are demonstrating gauge-invariance of the fermion mass shell in QED$_{2+1}$ in all orders of the perturbation theory.