Regularisation : many recipes, but a unique principle : Ward identities and Normalisation conditions. The case of CPT violation in QED

TL;DR

This paper demonstrates that, when properly defined with Ward identities and normalization conditions, QED with CPT violation does not generate a Chern-Simons term through radiative corrections, resolving controversy over its ambiguity.

Contribution

It establishes that a correctly formulated QED with CPT violation does not produce a Chern-Simons term, emphasizing the role of Ward identities and normalization conditions.

Findings

No Chern-Simons term appears under proper conditions

The absence of divergence is due to symmetry or non-renormalisation

Clarifies previous conflicting literature on CPT violation in QED

Abstract

We analyse the recent controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term : we prove that, if the theory is correctly defined through Ward identities and normalisation conditions, no Chern-Simons term appears, without any ambiguity. This is related to the fact that such a term is a kind of minor modification of the gauge fixing term, and then no renormalised. The past year literature on that subject is discussed, and we insist on the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry or some non-renormalisation theorem.