Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED

TL;DR

This paper reevaluates the radiative induction of a CPT and Lorentz violating Chern-Simons term in extended QED, emphasizing gauge invariance and analyzing both massless and massive models at one-loop order.

Contribution

It provides a detailed analysis of gauge symmetry preservation in the induction of the CS term, including non-perturbative insights and the role of transversality.

Findings

Gauge symmetry must be preserved by quantum corrections.

Transversality does not determine the CS coefficient.

Both massless and massive models are analyzed at one-loop.

Abstract

The radiative induction of the CPT and Lorentz violating Chern-Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector $b_\mu$ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by the quantum corrections. As a complement we obtain that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.