On the kinematics of the last Wigner particle

TL;DR

This paper explores the theoretical properties of Wigner's continuous spin particles, presenting a new scalar-like wave equation formulation that combines classical and quantum perspectives.

Contribution

It introduces a novel scalar-like first-quantized formulation of Wigner's continuous spin particles, integrating classical wave equations with modern prequantization methods.

Findings

Derivation of a scalar-like wave equation for continuous spin particles.

Connection between classical wave equations and quantum Poisson structures.

Insight into the mathematical structure of unobserved massless particles.

Abstract

Wigner's particle classification provides for "continuous spin" representations of the Poincar\'e group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by use of "Wigner rotations" in the textbooks' way, here we exhibit a scalar-like first-quantized form of those (bosonic) Wigner particles directly, by combining wave equations proposed by Wigner long ago with a recent prequantized treatment employing Poisson structures.