Physical (ir)relevance of ambiguities to Lorentz and CPT violation in QED

TL;DR

This paper examines the regularization and renormalization of Lorentz and CPT violating QED, highlighting the independence of the Chern-Simons coefficient and its relation to the ABJ anomaly, providing insights into the convergence of the induced term.

Contribution

It demonstrates that the Chern-Simons coefficient in Lorentz and CPT violating QED is an independent parameter and links it to the ABJ anomaly, clarifying its physical relevance.

Findings

The Chern-Simons coefficient is not fixed by gauge invariance.

A relation between Lorentz/CPT violation and the ABJ anomaly is established.

The convergence of the induced Chern-Simons term is explained.

Abstract

We discuss the regularization and renormalization of QED with Lorentz and CPT violation, and argue that the coefficient of the Chern-Simons term is an independent parameter not determined by gauge invariance. We also study these issues in a model with spontaneous breaking of Lorentz and CPT symmetries and find an explicit relation with the ABJ anomaly. This explains the observed convergence of the induced Chern-Simons term.