Radiatively-Induced Lorentz and CPT Violating Chern-Simons Term in QED

TL;DR

This paper calculates the radiatively induced Lorentz- and CPT-violating Chern-Simons term in QED, confirming previous linear results and showing higher order terms vanish, thus clarifying the structure of symmetry violation in the theory.

Contribution

It provides an all-orders calculation of the induced Chern-Simons term in Lorentz- and CPT-violating QED, confirming the linear approximation results and demonstrating the absence of higher order contributions.

Findings

The induced Chern-Simons term matches previous linear-in-b calculations.

Higher order terms in b vanish, simplifying the theoretical structure.

The result confirms the consistency of the Lorentz- and CPT-violating extension of QED.

Abstract

We calculate the induced Lorentz- and CPT-violating Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum electrodynamics with a $b_\mu\bar{\psi}\gamma^\mu\gamma_5\psi$ term. The result to all orders in $b$ coincides with the previous linear-in-$b$ calulation by Chung and Oh [hep-th/9812132] as well as Jackiw and Kosteleck\'{y} [Phys. Rev. Lett. {\bf 82}, 3572 (1999)], since all higher order terms vanish.