Gauge Invariance for Classical Massless Particles with Spin

TL;DR

This paper extends Wigner's classification to classical massless particles, showing that gauge invariance is essential for their phase space structure and exploring a classical Higgs mechanism.

Contribution

It introduces a classical analogue of gauge invariance for massless particles and connects the massless limit to a classical Higgs mechanism.

Findings

Phase space of massless particles requires gauge invariance for physical consistency

Classical Higgs mechanism derived from massless to massive particle transition

Phase space properties linked to electromagnetic gauge invariance

Abstract

Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincar\'e group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle version of the Higgs mechanism.