Generation of new symmetries from explicit symmetry breaking

N Dimakis

doi:10.1088/1742-6596/2090/1/012052

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.

Highlights

Symmetries play an important role in all aspects of theoretical physics [1]; from the fundamental level and small scales, to cosmology and the description of the universe
We are interested to see what happens to the classes of certain symmetries which are broken due to some parameter entering the Lagrangian; this is the scenario of an explicit symmetry breaking
It is well known that for null geodesics, when m = 0, all conformal Killing vectors (CKVs), Lξgμν = 2ω(x)gμν, are symmetries of the Lagrangian (6) and they generate linear in the momenta integrals of motion I = ξαpα, since it can be seen that dI dτ

Summary

Introduction

Symmetries play an important role in all aspects of theoretical physics [1]; from the fundamental level and small scales, to cosmology and the description of the universe. The second is dedicated to infinite dimensional symmetry groups, which give rise to differential or algebraic identities among the equations of motion, i.e. not all degrees of freedom are independent These symmetries are related to the existence of some gauge freedom in the respective system. If ε = 0 we may have some group A whose generators satisfy (2), while if ε = 0 the corresponding group changes to B for which it usually holds that B ⊂ A As it happens, both the symmetry criterion (2) and the conservation law requirement (5), define linear partial differential equations for the components of X and the function I respectively. We demonstrate this fact by examining closely two examples: firstly the motion of a free relativistic particle in a generic background metric and the motion in a Bogoslovsky-Finsler space-time

The free relativistic particle

Motion in a Bogoslovsky-Finsler space-time

Conclusions