### 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 |
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Article number | 016 |

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

Volume | 6 |

DOIs | |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- Noncommutative geometry
- Nonrelativistic spin

### ASJC Scopus subject areas

- Geometry and Topology
- Mathematical Physics
- Analysis

### Cite this

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

*6*, [016]. https://doi.org/10.3842/SIGMA.2010.016

**From noncommutative sphere to nonrelativistic spin.** / Deriglazov, Alexei A.

Research output: Contribution to journal › Article

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, vol. 6, 016. https://doi.org/10.3842/SIGMA.2010.016

}

TY - JOUR

T1 - From noncommutative sphere to nonrelativistic spin

AU - Deriglazov, Alexei A.

PY - 2010

Y1 - 2010

N2 - 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.

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.

KW - Noncommutative geometry

KW - Nonrelativistic spin

UR - http://www.scopus.com/inward/record.url?scp=84891448817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891448817&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2010.016

DO - 10.3842/SIGMA.2010.016

M3 - Article

VL - 6

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

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

SN - 1815-0659

M1 - 016

ER -