Generation of new symmetries from explicit symmetry breaking

TL;DR

This paper explores how explicit symmetry breaking in physical systems can paradoxically lead to the emergence of new symmetries or conserved quantities, demonstrated through relativistic particle models in curved and Finsler spacetimes.

Contribution

It introduces a novel perspective on symmetry breaking, showing it can generate new symmetries and conserved charges in specific relativistic contexts.

Findings

Nonlocal conserved charges emerge when conformal symmetry is broken.

Rational integrals of motion replace broken boost symmetries in Finsler spacetime.

Explicit symmetry breaking can lead to the creation of new symmetries.

Abstract

We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a nonzero mass breaks the symmetry of the conformal algebra of the metric, and the motion in a Bogoslovsky-Finsler space-time, where a Lorentz violation takes place. In the first case, new nonlocal conserved charges emerge in the place of those which were previously generated by the conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.