Causality and radiatively induced CPT violation

We consider quantum electrodynamics with an additional Lorentz- and CPT-violating axial-vector term in the fermionic sector and discuss the possibility that radiative corrections induce a Lorentz- and CPT-violating Chern–Simons-like term for the gauge field. From the requirement of causality and the assumed validity of perturbation theory, we conclude that the induced Chern–Simons-like term must be absent in the full quantum field theory.