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We introduce a new version of non-linear electrodynamics which is produced bya spontaneous symmetry breaking of Lorentz invariance induced by the non-zeroexpectation value of the electromagnetic field strength. The symmetry breakingpotential is argued to effectively arise from the integration of massive gaugebosons and fermions in an underlying fundamental theory. All possible choicesof 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 foran arbitrary vacuum. They present two types of dispersion relations. Onecorresponds to the case of the usual Maxwell electrodynamics with the standardpolarization properties of the fields. The other dispersion relation involvesanisotropies determined by the structure of the vacuum. The model is stable inthe small Lorentz invariance violation approximation. We have embedded ourmodel in the photon sector of the Standard Model Extension in order to setbounds for our parameters. The one-way anisotropic speed of light is calculatedfor a general vacuum and its isotropic component is strongly bounded by${\tilde \delta c}/c < 2 \times 10^{-32}$. The anisotropic violationcontribution is estimated by introducing an alternative definition for thedifference of the two-way speed of light in perpendicular directions $\Deltac$, which is also strongly bounded by ${\Delta c}/c < 10^{-32}$. Finally, wespeculate on the relation of the vacuum energy of the model with thecosmological constant and propose a connection between the vacuum fields andthe intergalactic magnetic fields.

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