Free massless particles and extended space-time algebra

TL;DR

This paper explores the symmetries of relativistic particles, showing that massless particles exhibit conformal invariance and an extended algebra, unlike massive particles which only have Poincare invariance.

Contribution

It reveals a new invariance in the massless particle action that allows extending the conformal algebra, highlighting different symmetry breaking mechanisms.

Findings

Massless particles have conformal symmetry in four dimensions.

A new invariance extends the conformal algebra for massless particles.

Two symmetry breaking mechanisms differentiate massive and massless cases.

Abstract

We study the space-time invariances of the relativistic particle action for both the massive and massless cases. While the massive action has only the invariances associated to the Poincare algebra, we find that the invariances of the massless action give rise to the conformal algebra in four dimensions. For the free massless particle, a new invariance of the action permits the construction of an extension of the conformal algebra. The conclusion is that two distinct symmetry breaking mechanisms are necessary to arrive at the Poincare algebra.