Consistency relations for an implicit<b><i>n</i></b>-dimensional regularization scheme

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 $\mathrm{CPT}$ violation in extended ${\mathrm{QED}}_{4},$ topological mass generation in three-dimensional gauge theories, the Schwinger model, and its chiral version.