From noncommutative sphere to nonrelativistic spin

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.

Original language	English
Article number	016
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	6
DOIs	https://doi.org/10.3842/SIGMA.2010.016
Publication status	Published - 2010

Keywords

Noncommutative geometry
Nonrelativistic spin

ASJC Scopus subject areas

Geometry and Topology
Mathematical Physics
Analysis

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10.3842/SIGMA.2010.016

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title = "From noncommutative sphere to nonrelativistic spin",

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.",

keywords = "Noncommutative geometry, Nonrelativistic spin",

author = "Deriglazov, {Alexei A.}",

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AB - 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.

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