Ambiguities versus gauge invariance in the calculation of the radiatively induced Chern-Simons shift in extended QED

The one-loop radiative correction arising from the Lorentz and CPT non-invariant fermionic sector of an extended version of quantum electrodynamics (QED) is explicitly evaluated by using a general calculational method. The possibility of Lorentz and CPT violations, of the Chern-Simons form, being radiatively induced are investigated. We show that from our results it is possible to recover the (ambiguous) value previously obtained by other authors. However, if we choose the interpretations for the divergent integrals in such a way that the usual QED U(1) gauge invariance is maintained in the calculated amplitudes, to be consistent with renormalizability, rigorous constraints emerge for the radiatively induced Chern-Simons term and consequently, a non-vanishing non-ambiguous value can be obtained.