Caroll-Field-Jackiw electrodynamics in the pre-metric framework

TL;DR

This paper embeds the Carroll-Field-Jackiw electrodynamics model into the pre-metric framework, revealing differences in energy-momentum tensors and explaining birefringence effects without relying on metric-dependent assumptions.

Contribution

It demonstrates how the CFJ model can be integrated into the pre-metric approach, clarifying the relation between their energy-momentum tensors and wave propagation characteristics.

Findings

CFJ energy-momentum tensor is a conserved closure of the pre-metric tensor.

Birefringence in CFJ is explained by extending the Fresnel equation with a derivative term.

Lorentz and CPT violation models are compatible with the pre-metric framework.

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 pre-metric approach recently developed by Hehl and Obukhov. This embedding turns out to be non-trivial. Particularly, the pre-metric 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 pre-metric one. Another problem is in the description of the birefringence effect, which in the pre-metric 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 non zero 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 pre-metric approach to electrodynamics. This correspondence can be useful for both constructions.