Dynamical symmetry breaking in Abelian geometrodynamics

Abstract

Abstract A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the Einstein-Maxwell stress-energy tensor, any stress-energy tensor in a local and covariant way, and allows for maximum simplification of the expression of the electromagnetic field, in any curved four-dimensional Lorentzian spacetime, allowing for the identification of its degrees of freedom in two local scalars. New isomorphisms are proved. A new internal-spacetime mapping is established using these new tetrads. It is possible to map the local group of electromagnetic gauge transformations into the transformation groups of tetrad vectors on two local orthogonal planes. The planes that diagonalize the stress-energy tensor. We will discuss through a first order perturbative formulation the local loss of symmetry when a source of electromagnetic and gravitational field interacts with an agent that perturbs the original geometry associated to the source. The loss of symmetry will be manifested by the tilting of these planes under the influence of an external agent. In this strict sense the original local symmetry will be lost, however a new symmetry will arise. The purpose of this report is to show that the geometrical manifestation of local gauge symmetries is dynamic.