Consistency Relations for an Implicit n-dimensional Regularization Scheme

TL;DR

This paper develops an n-dimensional implicit regularization scheme that handles divergences involving parity-violating objects without dimensional continuation, using symmetries to resolve ambiguities in one-loop calculations.

Contribution

It extends an implicit regularization method to n-dimensional space-time, enabling consistent treatment of parity-violating divergences without dimensional continuation.

Findings

Successfully applied to CPT violation in extended QED_4

Clarified topological mass generation in 3D gauge theories

Analyzed the Schwinger Model and its chiral version

Abstract

We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation. Special attention is paid to differences between integrals of the same degree of divergence, typical of one loop calculations, which are in principle undetermined. We show how to use symmetries in order to fix these quantities consistently. We illustrate with examples in which regularization plays a delicate role in order to both corroborate and elucidate the results in the literature for the case of CPT violation in extended $QED_4$, topological mass generation in 3-dimensional gauge theories and the Schwinger Model and its chiral version.