Extended QED with CPT violation : clarifying some controversies

TL;DR

This paper revisits debates on the generation of a Chern-Simons-like term in CPT-violating QED, analyzing the impact of Lagrangian division and the role of symmetries in divergence absence.

Contribution

It clarifies controversies by critically examining the role of Lagrangian division and symmetry arguments in CPT-violating QED.

Findings

The division of Lagrangian affects the interpretation of radiative corrections.

Absence of divergences requires symmetry or non-renormalisation theorems for explanation.

Maximal SO(3) symmetry does not resolve the controversy.

Abstract

We rediscuss the controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term. We analyse some consequences of the division of the Lagrangian density between "free part" and "interaction part". We also emphasize the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry or some non-renormalisation theorem and show that the so-called "unambiguous result" based upon "maximal SO(3) residual symmetry " does not offer a solution.