The Goldstone Theorem in non-linear electrodynamics

TL;DR

This paper develops a non-linear electrodynamics model with spontaneous Lorentz symmetry breaking, revealing Goldstone modes associated with zero permeability modes, and explores their properties and relationships.

Contribution

It introduces a novel non-linear electrodynamics framework based on vacuum expectation values of the field strength, extending the Goldstone theorem to this context.

Findings

Identification of zero modes as Goldstone modes

Explicit construction of Goldstone modes for specific vacua

Derived relationships among generalized permeabilities

Abstract

We construct a non-linear electrodynamics arising from the spontaneous Lorentz symmetry breaking triggered by a non-zero vacuum expectation value of the electromagnetic field strength, instead of the electromagnetic potential. The expansion of the corresponding action in terms of the physical photon excitations is naturally written in terms of generalized permeabilities, in a manner similar to when the polarization is expanded in terms of the susceptibilities when studying non-linear effects in standard optics. The new version of the Goldstone theorem is investigated and implies that the lowest order permeability, been the analogous of the mass matrix in the standard case, has zero modes. These are interpreted as the corresponding Goldstone modes of the model and they are explicitly constructed for one of the two choices of vacua that the theory admits. Further iterations of the method employed to obtain such theorem yield relationships among the generalized permeabilities. Some preliminary results regarding the splitting of the two degrees of freedom of the model into Goldstone and non-Goldstone modes are presented.