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

TL;DR

This paper explores a mechanism for dynamical symmetry breaking in an extended electromagnetism theory with electric and magnetic gauge fields, revealing non-trivial configurations and invariances that differ from standard Maxwell electromagnetism.

Contribution

It introduces a novel approach to symmetry breaking in U(1)xU(1) electromagnetism, demonstrating non-trivial field configurations and invariances related to Hodge duality and zero-field solutions.

Findings

Effective field configurations eliminate discontinuities in monopole presence.

Extended electromagnetism differs from standard Maxwell theory despite Maxwell's equations compatibility.

Zero-field configuration is gauge invariant and self-dual, serving as a preferred state.

Abstract

It is considered a mechanism of dynamical symmetry breaking for extended Ue(1)xUg(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 are absent. These fields regularity is achieved through corrections, inherited from the unbroken theory, to the standard definitions of electromagnetic fields and four-currents. 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)xUg(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 that has as self-dual point the field configuration corresponding to the zero-field equation. 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.