Dynamical symmetry breaking in geometrodynamics

TL;DR

This paper demonstrates that local gauge symmetries in geometrodynamics are dynamically lost and replaced by new symmetries through perturbations, revealing the evolving nature of gauge invariance in curved spacetime.

Contribution

It introduces a first-order perturbative approach to show the dynamic evolution and loss of local gauge symmetries in four-dimensional Lorentzian spacetimes.

Findings

Local gauge symmetries are lost via tilting of symmetry planes.

New symmetry planes emerge after perturbation.

The study proves a theorem on dynamic symmetry evolution.

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.