A Geometric Model of Arbitrary Spin Massive Particle

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, ${\mathcal{M}}^6={\mathbb{R}}^{3,1}\times S^2$. The system describes Zitterbewegung at the classical level. Together with explicitly realized Poincaré 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 Poincaré 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.

25 pages; v2: eq. (45.b) corrected

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