Consistency of an alternative CPT-odd and Lorentz-violating extension of QED

Abstract

We investigate an alternative CPT-odd Lorentz-breaking QED which includes the CFJ term of the Standard Model Extension (SME), writing the gauge sector in the action in a Palatini-like form, in which the vectorial field and the field-strength tensor are treated as independent entities. Interestingly, this naturally relaxes the condition of gauge invariance in the classical action. We study physical consistency aspects of the model both at classical and quantum levels.

Residual Gauge Invariance in a Massive Lorentz-Violating Extension of QED

“…This particular LVI extension of QED, in which the background vector of the Carroll-Field-Jackiw (CFJ) term is responsible for the mass tensor, was obtained in [61], with α = −1, ρ = 1, and μ 2 = 1. This was accomplished through a Palatini-type procedure, in which the F μν tensor and the gauge field were initially considered to be independent.…”

“…We recognize above the propagator for the model of [61], if we fix α = −1, ρ = 1, and μ 2 = 1. Interesting that the dispersion relations extracted from the denominator D, responsible for the massive modes, are not affected by the constant ρ.…”

“…Interesting that the dispersion relations extracted from the denominator D, responsible for the massive modes, are not affected by the constant ρ. This parameter only influences the modes coming from D. In [61], the physical consistency of the modes of propagation of the vector field was studied in detail. For now, let us study the effects of the constant ρ on the model and, for comparison, let us fix α = −1 and μ 2 = 1.…”

“…An alternative way of generating Lorentz-violating mass terms was investigated in [61], in which a Palatini-like formulation of the CFJ model was performed. Interestingly, this formulation, with the participation of the CFJ term, caused the emergence of an unusual mass contribution in the photon Lagrangian density.…”

“…These results looked intriguing, since the model from which we begin, in which F μν is treated as an independent field, has no any evidence of violation of gauge symmetry. In this paper, we study a more general version of the massive model obtained in [61] and show that there is a residual gauge invariance in the model obtained from the Palatini-like formulation.…”