Generalized Proca Equations and Vacuum Current from Breaking of U e ( 1 ) × U g ( 1 ) Gauge Symmetry

We study a U e (1) × U g (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 vacuum-expectation-value (vev) for the C field in the full U e (1) × U g (1) theory we obtain both a mass term and a vacuum current. By considering the broken electric theory U e (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 pseudo-photon sector due to its vev, the effective theory for the standard photon still preserves Lorentz invariance.