Extended QED with CPT violation: Clarifying some controversies

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 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.