On the effective lagrangian in spinor electrodynamics with added violation of Lorentz and CPT symmetries

TL;DR

This paper investigates how adding Lorentz and CPT symmetry-violating axial vector couplings in spinor electrodynamics affects the one-loop effective action, finding no radiative induction of the Chern-Simons term and CPT invariance in the approximation.

Contribution

It provides a detailed calculation of the effective action with axial vector coupling, showing the absence of Chern-Simons term induction and CPT violation at one-loop order.

Findings

Chern-Simons term is not radiatively induced.

Effective action remains CPT invariant.

Calculations performed up to second order in axial vector.

Abstract

We consider quantum electrodynamics with additional coupling of spinor fields to the space-time independent axial vector violating both Lorentz and CPT symmetries. The Fock-Schwinger proper time method is used to calculate the one-loop effective action up to the second order in the axial vector and to all orders in the space-time independent electromagnetic field strength. We find that the Chern-Simons term is not radiatively induced and that the effective action is CPT invariant in the given approximation.