Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 016, 8 pages      arXiv:0911.2592      http://dx.doi.org/10.3842/SIGMA.2010.016
Contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries

From Noncommutative Sphere to Nonrelativistic Spin

Alexei A. Deriglazov
Dept. de Matematica, ICE, Universidade Federal de Juiz de Fora, MG, Brazil

Received November 12, 2009, in final form January 26, 2010; Published online February 04, 2010

Abstract
Reparametrization invariant dynamics on a sphere, being parameterized by angular momentum coordinates, represents an example of noncommutative theory. It can be quantized according to Berezin-Marinov prescription, replacing the coordinates by Pauli matrices. Following the scheme, we present two semiclassical models for description of spin without use of Grassman 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.

Key words: noncommutative geometry; nonrelativistic spin.

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