Induced Lorentz- and CPT-violating Chern-Simons term in QED: Fock-Schwinger proper time method

TL;DR

This paper uses the Fock-Schwinger proper time method to calculate the induced Chern-Simons term in Lorentz- and CPT-violating QED, confirming previous linear-in-b results to all orders in b.

Contribution

It provides a nonperturbative calculation of the induced Chern-Simons term in Lorentz- and CPT-violating QED using the Fock-Schwinger proper time method, matching recent linear-in-b results.

Findings

Result matches linear-in-b calculations by others.

Calculation valid to all orders in b.

Confirms previous perturbative results nonperturbatively.

Abstract

Using the Fock-Schwinger proper time method, we calculate the induced 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. Our result to all orders in $b$ coincides with a recent linear-in-$b$ calculation by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by Chung [Phys. Lett. {\bf B461} (1999) 138] and P\'{e}rez-Victoria [Phys. Rev. Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with the nonperturbative-in-$b$ propagator.