Effective Electric and Magnetic Local Actions for Ue(1)× Ug(1) Electromagnetism: Hodge Duality and Zero-Field Equation

Electromagnetism, Dynamical Symmetry Breaking, pseudo-photons, Zero Field Equation; packs: 03.50.De,11.15,-q,40. In this work it is considered a mechanism of dynamical symmetry breaking for extended Ue(1)×Ug(1) containing, one vector gauge field A (photon) and one pseudo-vector gauge field C (pseudo-photon). By choosing a particular solution of the equations of motion we obtain a functional description of either field in terms of the other one. In this way we obtain non-trivial configurations C = C(A) or A = A(C) such that, in the effective broken theories containing only one gauge field, the usual field discontinuities in the presence of both electric and magnetic monopoles (Dirac string or Wu-Yang non-trivial fiber-bundle) are absent. These fields regularity is achieved through corrections, inherited from the unbroken theory, to the standard definitions of electromagnetic fields and fourcurrents. Based in these results we also demonstrate non-triviality of the unbroken theory, in the presence of both electric and magnetic four-currents, there are no trivial solutions compatible with the equations of motion for both fields. Moreover we demonstrate that, although in complete agreement with the Maxwell equations, extended Ue(1)×Ug(1) electromagnetism is not equivalent to the standard variational U(1) Maxwell electromagnetism. We further show that the unbroken theory is invariant under a combination of Hodge dualities for the gauge connections, F → ǫ̂∗G and G → −ǫ̂∗F (ǫ̂ = ±1), that has as self-dual point, the field configuration corresponding to the zero-field equation C̃ = −ǫ̂A. In addition this condition has the particularity of being the only configuration compatible with the mechanism of dynamical symmetry breaking proposed here that is also gauge invariant in the unbroken theory. These characteristics justify the zero-field equation as being a preferred configuration.