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

We consider a U(1)×U(1) Electric-Magnetic theory with minimal coupling between both gauge fields A and C. We consider two possible mechanism of symmetry breaking that generate generalized Proca masses for the gauge field A. By considering a vacuum-expectation-value for the C field in the full U(1) × U(1) theory we obtain both a mass term and a vacuum current. By considering the broken electric theory U(1) we obtain a remaining free field on the solution for C, upon a vev to this remaining field we obtain only a mass term. The interpretation for the vev is given in terms of constant currents and holonomy cycles of the underlying space manifold. The number of degrees of freedom before and after gauge symmetry breaking are discussed, similarly to Schwinger and Anderson we consider the gauge freedom to constitute degrees of freedom that upon gauge symmetry breaking by non trivial vacuum currents hold three massive photons. PACS: 40., 03.50.De, 11.15.-q, 12.60.Nz