Gauge Invariance of QED$_{2+1}$

TL;DR

This paper investigates gauge invariance in (2+1)-dimensional QED, demonstrating that with Proca mass regularization, the physical sector remains gauge-invariant and well-defined across various gauges in all perturbation orders.

Contribution

It shows that Proca mass regularization ensures gauge-invariant fermion mass and a well-defined physical mass shell in QED$_{2+1}$, including in different gauge choices.

Findings

Gauge invariance of fermion mass is maintained with Proca regularization.

Physical mass shell is well-defined in all orders of perturbation theory.

Physical sector remains gauge-independent in multiple gauge choices.

Abstract

The problem of gauge invariance of the physical sector of (2+1)-dimensional Maxwell-Chern-Simons quantum electrodynamics (QED$_{2+1}$) is studied. It is shown that using Proca mass term for the infrared regularization one obtains gauge-invariant fermion mass and the physical mass shell of QED$_{2+1}$ is well-defined in all orders of the perturbation theory. We are demonstrating also a class of gauges in the framework of QED$_{2+1}$, including transversal and Feynman-like ones, where the physical sector is well defined and independent of the gauge parameter.