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 | |
| Publication status | Published - 2010 |
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Keywords
- Noncommutative geometry
- Nonrelativistic spin
ASJC Scopus subject areas
- Geometry and Topology
- Mathematical Physics
- Analysis
Cite this
From noncommutative sphere to nonrelativistic spin. / Deriglazov, Alexei A.
In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 6, 016, 2010.Research output: Contribution to journal › Article
}
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 -