Remarks on the renormalization properties of Lorentz and CPT violating quantum electrodynamics

TL;DR

This paper demonstrates the all-order renormalizability of Lorentz and CPT violating QED using algebraic techniques, identifying the renormalization parameters and analyzing the behavior of the Lorentz violating terms.

Contribution

It provides a rigorous proof of the renormalizability of Lorentz and CPT violating QED and details the renormalization parameters, including the non-renormalization of the Chern-Simons-like term.

Findings

The original QED has three independent renormalization parameters.

The Lorentz violating sector requires nineteen independent parameters for renormalization.

The Chern-Simons-like term does not undergo renormalization.

Abstract

In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz and CPT violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz violating sector can be renormalized by nineteen independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize. One-loop computations are also presented and compared with the existing literature.