Radiatively induced finite and (un)determined Chern-Simons-like terms

TL;DR

This paper investigates the quantum correction-induced Chern-Simons-like terms in extended QED, revealing ambiguities and potential resolutions through different regularization schemes and approaches to the fermion propagator.

Contribution

It compares approaches to induce Chern-Simons-like terms in extended QED, highlighting how different methods affect the results and discussing ambiguity resolution.

Findings

Different approaches yield distinct results within the same regularization scheme.

Modified derivative expansion and alternative regularization can reconcile results.

Proper treatment of fermion propagator may eliminate ambiguities.

Abstract

The problem of Chern-Simons-like term induction via quantum corrections in four-dimensions is investigated in two different cases. In the first case, we consider two distinct approaches to deal with the exact fermion propagator of the extended QED theory up to the first order in the $b$-coefficient. We find different results for distinct approaches in the same regularization scheme. In the second case, we show that when we use a modified derivative expansion method and another regularization scheme, we obtain a result that exactly coincides with one of the results obtained in the former case. This seems to imply an ambiguity absence as one treats the fermion propagator and the self-energy tensor properly.