Carroll-Field-Jackiw electrodynamics in the premetric framework

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Abstract
We analyze the Carroll-Field-Jackiw (CFJ) modification of electrodynamics reformulated as the ordinary Maxwell theory with an additional special axion field. In this form, the CFJ model appears as a special case of the premetric approach recently developed by Hehl and Obukhov. This embedding turns out to be nontrivial. Particularly, the premetric energy-momentum tensor does not depend on the axion. This is in contrast to the CFJ energy-momentum tensor which involves the axion addition explicitly. We show that the relation between these two quantities is similar to the correspondence between the Noether conserved tensor and the Hilbert symmetric tensor. As a result the CFJ energy-momentum tensor appears as the unique conserved closure of the premetric one. Another problem is in the description of the birefringence effect, which in the premetric framework does not depend on the axion. The comparison with the CFJ model shows that the corresponding wave propagation (Fresnel) equation has to be extended by a derivative term, which is nonzero for the axion field. In this way, the CFJ birefringence effect is derived in the metric-free approach. Consequently the Lorentz and CPT violating models can be embedded without contradictions in the premetric approach to electrodynamics. This correspondence can be useful for both constructions.