Consistency of an alternative CPT-odd and Lorentz-violating extension of QED

Abstract

We investigate an alternative CPT-odd Lorentz-breaking QED which includes the Carroll–Field–Jackiw (CFJ) term of the Standard Model Extension (SME), writing the gauge sector in the action in a Palatini-like form, in which the vectorial field and the field-strength tensor are treated as independent entities. Interestingly, this naturally induces a Lorentz-violating mass term in the classical action. We study physical consistency aspects of the model both at classical and quantum levels.