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A geometric model of the arbitrary spin massive particle. (English) Zbl 0985.81564

Summary: A new model of the relativistic massive particle with arbitrary spin (the \((m,s)\) particle) is suggested. The configuration space of the model is the product of Minkowski space and a two-dimensional sphere: \({\mathcal M}^6=R^{3,1}\times S^2\). 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.

MSC:

81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81R25 Spinor and twistor methods applied to problems in quantum theory
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