Dynamical symmetry breaking in geometrodynamics
Alcides Garat
TL;DR
This work reframes dynamical symmetry breaking in curved spacetime electromagnetism as a geometric evolution: local gauge symmetries act as local Lorentz transformations on two orthogonal blades $LB1$ and $LB2$, and external perturbations tilt these planes to generate new blades with corresponding symmetry axes. A first-order perturbative geometrodynamics framework is developed, employing tetrads that locally diagonalize the stress-energy tensor into blades and analyzing how the planes and associated energy–momentum currents evolve, with the Reissner–Nordström geometry serving as a concrete example. A central result is a dynamic symmetry-evolution theorem linking curvature changes to evolving local planes of symmetry and to a reconfiguration of conserved currents, complemented by appendices that establish current-conservation constraints on the original and perturbed blades and detail the perturbative covariant-derivative machinery. The findings offer a curvature-based analogue to dynamical symmetry breaking, providing geometric insights that could illuminate how external interactions shape local symmetries in classical gravitational–electromagnetic systems and potentially relate to broader mass-generation mechanisms.
Abstract
We will analyze 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. As the local gauge symmetry in Abelian or even non-Abelian field structures in four-dimensional Lorentzian spacetimes is displayed through the existence of local planes of symmetry that we will refer to as blades one and two, 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. We will be able to prove in this way that the new blades at the same point will correspond ''after the tilting generated by perturbation" to a new symmetry. The purpose of this paper is to show that the geometrical manifestation of local gauge symmetries is dynamic. Despite the fact that the local original symmetries will be lost, new symmetries will arise. A dynamic evolution of local symmetries will be evidenced. This result will produce a new theorem on dynamic symmetry evolution.