Is a particle an irreducible representation of the Poincar\'e group?

TL;DR

This paper critically examines the common identification of particles as irreducible Poincaré group representations, highlighting issues with this view and proposing an alternative characterization that applies across relativistic and non-relativistic contexts.

Contribution

The paper challenges Wigner's identification of particles with irreducible Poincaré representations and offers a new, more comprehensive definition linking particles to algebraic relations of position, momentum, and spin.

Findings

Objections to the adequacy of Wigner's identification for interacting particles.

An alternative particle characterization applicable in various spacetime settings.

A theorem connecting Poincaré generator decomposition with canonical algebraic relations.

Abstract

The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it is often taken as, or claimed to be, a definition. My aims in this paper are to: (i) clarify, and partially defend, the guiding ideas behind this identification; (ii) raise objections to its being an adequate definition; and (iii) offer a rival characterisation of particles. My main objections to Wigner's identification appeal to the problem of interacting particles, and to alternative spacetimes. I argue that the link implied in Wigner's identification, between a spacetime's symmetries and the generator of a particle's space of states, is at best misleading, and that there is no good reason to link the generator of a particle's space of states to symmetries of any kind. I propose an alternative characterisation of particles, which captures both the relativistic and non-relativistic setting. I further defend this proposal by appeal to a theorem which links the decomposition of Poincar\'e generators into purely orbital and spin components with canonical algebraic relations between position, momentum and spin.