A Note on the Radiatively Induced Lorentz and CPT Violated Chern-Simons-like Term in the Extended Quantum Electrodynamics

TL;DR

This paper clarifies the origin of ambiguity in the radiatively induced Chern-Simons-like term in extended QED, emphasizing the role of regularization schemes rather than fermionic propagator approximations.

Contribution

It demonstrates that the ambiguity is due to regularization scheme choices and confirms the result using 't Hooft-Veltman dimensional regularization.

Findings

Ambiguity is unrelated to fermionic propagator approximation.

Reproduces gauge symmetry analysis result with dimensional regularization.

Highlights regularization scheme choice as the source of ambiguity.

Abstract

We show that the ambiguity for the Chern-Simons-like term induced from quantum correction in the extended QED should have nothing to do with the approximation on the exact fermionic propagator, contradictory to the claim in Ref.[19]. Further, we investigate the induced Chern-Simons-like term using the original 't Hooft-Veltman dimensional regularization and reproduce the result obtained by gauge symmetry analysis. This fact demonstrates that the origin of the ambiguity should lie in different choices on regularization schemes.