Perturbative generation of photon Lorentz violating terms from a pseudo-tensor Lorentz-breaking extension of QED

We consider an extended QED with the addition of a dimension-five Lorentz-breaking coupling between spinor and gauge fields, involving a pseudo-tensor ${\kappa }^{\mu \nu \lambda \rho }$. The specific form of the Lorentz violating coupling considered by us have been suggested in other works, and some of its consequences at the classical level were already studied. Here, we investigate the consequences of this specific form of Lorentz violation at the quantum level, evaluating the one loop corrections to the gauge field two-point function, both at zero and at finite temperature. We relate the terms that are generated by quantum corrections with the photon sector of the Standard Model Extension, discussing the possibility of establishing experimental bounds on $k^{\mu \nu \rho \sigma }$. From the dispersion relations in the resulting theory, we discuss its consistency from the causality viewpoint.