Induced Lorentz-Violating Chern-Simons Term in QED and Anomalous Contributions to Effective Action Expansions

TL;DR

This paper presents a unified method to calculate anomalous contributions in quantum field theories, specifically deriving the induced Lorentz-violating Chern-Simons term in QED by addressing ambiguities related to noncommutative operators.

Contribution

It introduces a covariant-derivative expansion technique to uniquely determine the induced Chern-Simons term in Lorentz and CPT violating QED, resolving previous ambiguities.

Findings

Derived the induced Chern-Simons term from Lorentz and CPT violation in QED.

Resolved ambiguities by properly accounting for noncommutativity of fields and derivatives.

Identified a non-Feynman diagram anomalous contribution to the vacuum polarization tensor.

Abstract

I present a unified formulation of anomalous contributions in quantum field theories by calculating directly the effective action using the background field and covariant-derivative expansion technique. I use this method to determine uniquely the induced Chern-Simons term from the a Lorentz and CPT violating term in fermion QED Lagrangian. The outstanding ambiguity is resolved by properly taken into account the noncommutivity of $A$ and $\partial$. The resulting vacuum polarization tensor acquires a non-Feynman diagram anomalous contribution which accounts for the discrepancy between the present calculation and the other calculations.