Induced Lorentz & CPT invariance violations in QED

We consider QED in a constant axial--vector background (\AE ther). Further Lorentz invariance violations (LIV) occur owing to radiative corrections. A detailed study of the phenomenology of this model is carried out, clarifying important issues related to the various regularisations employed, with a particular emphasis on the induced photon mass. To this concern, the crucial physical meaning of the large ultraviolet cut--off induced by LIV is exploited. Finally, the finite temperature radiative corrections are evaluated and the various experimental bounds on the parameters of the model are thoroughly discussed.