Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework

TL;DR

This paper introduces a novel momentum space regularization framework for quantum field theories, especially useful for dimension-specific theories and handling infinities without analytic continuation, demonstrating its consistency with anomalies and CPT violation.

Contribution

It presents a new regularization method in momentum space that manages infinities and local terms without analytic continuation, applicable to parity-violating theories.

Findings

Consistent calculation of the CPT violating Chern-Simons term.

Successful analysis of the Adler-Bardeen-Bell-Jackiw anomaly.

Framework handles finite radiative corrections effectively.

Abstract

This is the second in a series of two contributions in which we set out to establish a novel momentum space framework to treat field theoretical infinities in perturbative calculations when parity-violating objects occur. Since no analytic continuation on the space-time dimension is effected, this framework can be particularly useful to treat dimension-specific theories. Moreover arbitrary local terms stemming from the underlying infinities of the model can be properly parametrized. We (re)analyse the undeterminacy of the radiatively generated CPT violating Chern-Simons term within an extended version of $QED_4$ and calculate the Adler-Bardeen-Bell-Jackiw triangle anomaly to show that our framework is consistent and general to handle the subtleties involved when a radiative corretion is finite.