Bimetric QED

TL;DR

This paper explores the quantisation and renormalisation of Bimetric QED, a Lorentz symmetry breaking extension of QED where photons and electrons propagate differently, leading to complex dispersion relations and birefringence effects.

Contribution

It introduces a novel bimetric extension of QED, analyzes its renormalisation, and classifies Lorentz symmetry breaking via Petrov types, including explicit dispersion relations.

Findings

Derived explicit photon dispersion relations for each Petrov class.

Identified renormalisation group flows and fixed points for model parameters.

Showed that renormalisation can adjust metrics and Lorentz symmetry breaking tensors.

Abstract

We study, as a model of Lorentz symmetry breaking, the quantisation and renormalisation of an extension of QED in a flat spacetime where the photons and electrons propagate differently and do not share the same lightcone. We will refer to this model as Bimetric QED (BIMQED). As a preliminary we discuss the formulation of electrodynamics in a pre-metric formalism showing nevertheless that there is, on the basis of a simple criteron, a preferred metric. Arising from this choice of metric is a Weyl-like tensor (WLT). The Petrov classification of the WLT gives rise to a corresponding classification of Lorentz symmetry breaking. We do not impose any constraint on the strength of the symmetry breaking and are able to obtain explicit dispersion relations for photon propagation in each of the Petrov classes. The associated birefringence appears in some cases as two distinct polarisation dependent lightcones and in other cases as a a more complicated structure that cannot be disentangled in a simple way. We show how in BIMQED the renormalisation procedure can, in addition to its effect on standard parameters such as charge and mass, force the renormalisation of the metrics and the WLT. Two particularly tractable cases are studied in detail for which we can obtain renormalisation group flows for the parameters of the model together with an analysis of fixed point structure. Of course these results are consistent with previous studies but we are not constrained to treat Lorentz symmetry breaking as necessarily weak. As we found in a previous study of a scalar field theory model an acceptable causal structure for the model imposes constraints on relationship between the various lightcones in BIMQED.