A Geometric Model of Arbitrary Spin Massive Particle

TL;DR

This paper introduces a classical and quantum model for massive particles with arbitrary spin, using a geometric configuration space and gauge symmetries, leading to relativistic wave equations for spin-$s$ fields.

Contribution

It presents a novel geometric model with gauge invariance for arbitrary spin particles, connecting classical constraints to quantum wave equations.

Findings

Model describes Zitterbewegung at classical level.

Quantization yields relativistic wave equations for spin-$s$ fields.

Configuration space is Minkowski space times a 2-sphere.

Abstract

A new model of relativistic massive particle with arbitrary spin (($m,s$)-particle) is suggested. Configuration space of the model is a product of Minkowski space and two-dimensional sphere, ${\cal M}^6 = {\Bbb R}^{3,1} \times S^2$. The system describes Zitterbewegung at the classical level. Together with explicitly realized Poincar\'e symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first-class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase-space counterparts of the Casimir operators of the Poincar\'e group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin-$s$ field.