The Goldstone Theorem in non-linear electrodynamics

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.

6 pages (double column), no figures, latex, epl2. Section II includes the correct prescription to study the linearized approximation. Previous section VI is replaced by a preliminary discussion on how the two degrees of freedom of the model split into Goldstone and non-Goldstone modes. Section VII has been slightly modified accordingly

References in corpus (4)

• Spontaneous Lorentz Violation: Non-Abelian Gauge Fields as Pseudo-Goldstone Vector Bosons
• Deriving Gauge Symmetry and Spontaneous Lorentz Violation
• The invariants of the electromagnetic field
• Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking

Cited by in corpus (6)

• Local effects of the quantum vacuum in Lorentz-violating electrodynamics
• Casimir effect between ponderable media as modeled by the standard model extension
• The full CPT-even photon sector of the Standard Model Extension at finite temperature
• Testing Lorentz- and CPT-invariance with ultracold neutrons
• (2+1)-dimensional Static Cyclic Symmetric Traversable Wormhole: Quasinormal Modes and Causality
• Degenerate behavior in nonlinear vacuum electrodynamics