Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics

TL;DR

This paper investigates the nonperturbative structure of the Chern-Simons term in Lorentz- and CPT-violating QED, showing gauge invariance can be preserved with a Pauli-Villars regulator, allowing for a nonzero or zero coefficient.

Contribution

It demonstrates that gauge invariance can be maintained using a Pauli-Villars regulator in Lorentz- and CPT-violating QED, permitting a nonzero Chern-Simons coefficient.

Findings

The Chern-Simons coefficient can be zero or nonzero.

Gauge invariance can be preserved with a Pauli-Villars regulator.

The nonperturbative theory yields a definite Chern-Simons value.

Abstract

We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentz- and CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the nonperturbative theory appears to generate a definite value. However, the CPT-even radiative corrections in this same formulation of the theory generally break gauge invariance. We show that gauge invariance may yet be preserved through the use of a Pauli-Villars regulator, and, contrary to earlier expectations, this regulator does not necessarily give rise to a vanishing Chern-Simons term. Instead, two possible values of the Chern-Simons coefficient are allowed, one zero and one nonzero. This formulation of the theory therefore allows the coefficient to vanish naturally, in agreement with experimental observations.