On the consistency of Lorentz invariance violation in QED induced by   fermions in constant axial-vector background
  We show for the first time that the induced parity--even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light--like cosmic anisotropy axial--vector or for a time--like one, when in the presence of a bare photon mass. 
J. Alfaro, A.A. Andrianov, M. Cambiaso, P. Giacconi and R. Soldati