2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183246We 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.10 pages, revised for publication in Phys.Lett. BHigh Energy Physics - TheoryAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - PhenomenologyOn the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector backgroundtext