1305.5415 (C. A. Escobar et al.)

The Goldstone Theorem in non-linear electrodynamics    [PDF]

C. A. Escobar, L. F. Urrutia

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 Goldstone theorem is subsequently deduced yielding 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 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. We also state the conditions under which the model induces Lorentz invariance violating corrections to standard linear electrodynamics.

View original: http://arxiv.org/abs/1305.5415