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Nonrelativistic spin: á 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:
81S05Commutation relations (quantum theory)
81R25Spinor and twistor methods in quantum theory