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.Comment: 17 pages, LaTeX, v.2, minor changes, Eqs.(5.12) and (5.13) added,
misprints correcte