Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED

TL;DR

This paper investigates a nonperturbative approach to Lorentz-violating QED and finds that it fails to maintain gauge invariance at higher orders, questioning the significance of the induced Chern-Simons term.

Contribution

It demonstrates that a specific nonperturbative value of the Chern-Simons coefficient does not preserve gauge invariance in Lorentz-violating QED.

Findings

Nonperturbative formulation assigns a definite Chern-Simons coefficient.

Gauge invariance is broken at higher orders.

The specific nonperturbative value is not physically significant.

Abstract

We consider a Lorentz-violating modification to the fermionic Lagrangian of QED that is known to produce a finite Chern-Simons term at leading order. We compute the second order correction to the one-loop photon self-energy in the massless case using an exact propagator and a nonperturbative formulation of the theory. This nonperturbative theory assigns a definite value to the coefficient of the induced Chern-Simons term; however, we find that the theory fails to preserve gauge invariance at higher orders. We conclude that the specific nonperturbative value of the Chern-Simons coefficient has no special significance.