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Nonrelativistic spin: à la Berezin-Marinov quantization on a sphere. (English) Zbl 1202.81123

Summary: Reparametrization invariant dynamics on a sphere, being parametrized by angular momentum coordinates, represents an appropriate framework for semiclassical description of nonrelativistic spin. The space can be quantized according to Berezin-Marinov prescription, replacing the coordinates by Pauli matrices. Following the scheme, we present two semiclassical models for describing spin without the use of Grassmann variables. The first model implies Pauli equation upon the canonical quantization. The second model produces nonrelativistic limit of the Dirac equation implying correct value for the electron spin magnetic moment.

MSC:

81S05 Commutation relations and statistics as related to quantum mechanics (general)
81R25 Spinor and twistor methods applied to problems in quantum theory
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References:

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