We study a Ue(1) × Ug(1) Electric-Magnetic theory with minimal coupling between both gauge fields A (photon) and C (pseudo-photon). We consider two possible mechanism of symmetry breaking that generate generalized Proca masses for the gauge field A. By considering a vacuumexpectation-value (vev) for the C field in the full Ue(1) ×Ug(1) theory we obtain both a mass term and a vacuum current. By considering the broken electric theory Ue(1) we obtain as a solution for the C field a remaining free field c such that, upon be given a vev, renders a mass term for the photon field A. The interpretation for the vev is given in terms of constant currents and homology cycles of the underlying space manifold. The number of degrees of freedom, before and after gauge symmetry breaking, are discussed. As a particular case of this construction the authors have already shown that this mechanism reproduces the Schwinger-Anderson mechanism such that upon gauge symmetry breaking due to non trivial vacuum generates mass for the standard photon (plasmon). We show that, although generally, Lorentz symmetry may be broken in the pseudophoton sector due to its vev, the effective theory for the standard photon still preserves Lorentz invariance.

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Abstract: In this article it is studied, at variational level, a mathematical setup given by the Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensions within the framework of dimensional reduced Ue(1) × Ug(1) extended electromagnetism with both vector gauge fields (photons) and pseudo-vector gauge fields (pseudo-photons) such that both magnetic and electric vortexes coexist in the planar system. This model exhibits explicit planar P and T discrete symmetries being the Hall conductivity consistently a tensor and the Dirac quantization on the electric and magnetic coupling constants is equivalent to the quantization of magnetic flux. It is also discussed a thickening to 4-dimensions of the model with explicit 4-dimensional P violation which allows either for electric and magnetic charge separation, either for the Meissner effect. Although mathematically consistent, the electromagnetic field content for this model does not coincide with the standard Hall effect being present an extra orthogonal electric and longitudinal magnetic fields. c ○ Electronic Journal of Theoretical Physics. All rights reserved.