On the effective lagrangian in spinor electrodynamics with added violation of Lorentz and CPT symmetries

We consider quantum electrodynamics with additional coupling of spinor fields to the space-time independent axial vector violating both Lorentz and CPT symmetries. The Fock-Schwinger proper time method is used to calculate the one-loop effective action up to the second order in the axial vector and to all orders in the space-time independent electromagnetic field strength. We find that the Chern-Simons term is not radiatively induced and that the effective action is CPT invariant in the given approximation.