Lorentz and CPT violation in QED revisited: A missing analysis

TL;DR

This paper rigorously proves that a CPT-odd, Lorentz-violating Chern-Simons-like term is not generated in QED with an axial fermion current coupling to a constant vector, using algebraic renormalization.

Contribution

It provides a regularization-independent proof that such Lorentz and CPT violating terms are not radiatively induced in this QED framework.

Findings

No radiative induction of the Chern-Simons-like term

Validates the stability of Lorentz and CPT symmetry in this model

Uses algebraic renormalization to achieve regularization independence

Abstract

We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field $b$, in the framework of algebraic renormalization -- a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector $b$.