Is a particle an irreducible representation of the Poincaré group?

• URL: http://arxiv.org/abs/2410.02354v1
• Date: Thu, 3 Oct 2024 10:06:00 GMT
• Title: Is a particle an irreducible representation of the Poincaré group?
• Authors: Adam Caulton,
• Abstract summary: The claim that a particle is an irreducible representation of the Poincar'e group is 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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