The Goldstone theorem in non-linear electrodynamics
1 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México - A. Postal 70-543, 04510 México D.F., México
2 Facultad de Física, Pontificia Universidad Católica de Chile - Casilla 306, Santiago 22, Chile
Received: 14 April 2014
Accepted: 17 April 2014
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.
PACS: 11.30.Qc – Spontaneous and radiative symmetry breaking / 11.30.Cp – Lorentz and Poincaré invariance / 11.10.Lm – Nonlinear or nonlocal theories and models
© EPLA, 2014