Gauge invariant non-linear electrodynamics motivated by a spontaneous breaking of the Lorentz symmetry

TL;DR

This paper proposes a new non-linear electrodynamics model with spontaneous Lorentz symmetry breaking, analyzing its wave solutions, stability, and experimental bounds, and exploring its cosmological implications.

Contribution

It introduces a Lorentz-violating non-linear electrodynamics model derived from fundamental theory, with detailed analysis of wave solutions and experimental constraints.

Findings

Two types of dispersion relations identified.

Strong bounds on anisotropic light speed violations.

Model remains stable under small Lorentz violation.

Abstract

We introduce a new version of non-linear electrodynamics which is produced by a spontaneous symmetry breaking of Lorentz invariance induced by the non-zero expectation value of the electromagnetic field strength. The symmetry breaking potential is argued to effectively arise from the integration of massive gauge bosons and fermions in an underlying fundamental theory. All possible choices of the vacuum lead only to the remaining invariant subgroups T(2) and HOM(2). We explore the plane wave solutions of the linearized sector of the model for an arbitrary vacuum. They present two types of dispersion relations. One corresponds to the case of the usual Maxwell electrodynamics with the standard polarization properties of the fields. The other dispersion relation involves anisotropies determined by the structure of the vacuum. The model is stable in the small Lorentz invariance violation approximation. We have embedded our model in the photon sector of the Standard Model Extension in order to set bounds for our parameters. The one-way anisotropic speed of light is calculated for a general vacuum and its isotropic component is strongly bounded by ${\tilde \delta c}/c < 2 \times 10^{-32}$. The anisotropic violation contribution is estimated by introducing an alternative definition for the difference of the two-way speed of light in perpendicular directions $\Delta c$, which is also strongly bounded by ${\Delta c}/c < 10^{-32}$. Finally, we speculate on the relation of the vacuum energy of the model with the cosmological constant and propose a connection between the vacuum fields and the intergalactic magnetic fields.