Abstract
We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both Γ-matrices and the relativistic spin tensor are produced through the canonical quantization of the classical variables which parametrize the properly constructed relativistic spin surface. Although there is no mass-shell constraint in our model, our particle's speed cannot exceed the speed of light. The classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. In particular, the position variable experiences Zitterbewegung in noninteracting theory. The classical equations for the spin tensor are the same as those of the Barut-Zanghi model of a spinning particle.
| Original language | English |
|---|---|
| Pages (from-to) | 398-406 |
| Number of pages | 9 |
| Journal | Annals of Physics |
| Volume | 327 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Feb 2012 |
| Externally published | Yes |
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Keywords
- Dirac equation
- Local (gauge) symmetries
- Relativistic spin
- Theories with constraints
- Zitterbewegung
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
A semiclassical description of relativistic spin without the use of Grassmann variables and the Dirac equation. / Deriglazov, A. A.
In: Annals of Physics, Vol. 327, No. 2, 01.02.2012, p. 398-406.Research output: Contribution to journal › Article
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TY - JOUR
T1 - A semiclassical description of relativistic spin without the use of Grassmann variables and the Dirac equation
AU - Deriglazov, A. A.
PY - 2012/2/1
Y1 - 2012/2/1
N2 - We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both Γ-matrices and the relativistic spin tensor are produced through the canonical quantization of the classical variables which parametrize the properly constructed relativistic spin surface. Although there is no mass-shell constraint in our model, our particle's speed cannot exceed the speed of light. The classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. In particular, the position variable experiences Zitterbewegung in noninteracting theory. The classical equations for the spin tensor are the same as those of the Barut-Zanghi model of a spinning particle.
AB - We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both Γ-matrices and the relativistic spin tensor are produced through the canonical quantization of the classical variables which parametrize the properly constructed relativistic spin surface. Although there is no mass-shell constraint in our model, our particle's speed cannot exceed the speed of light. The classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. In particular, the position variable experiences Zitterbewegung in noninteracting theory. The classical equations for the spin tensor are the same as those of the Barut-Zanghi model of a spinning particle.
KW - Dirac equation
KW - Local (gauge) symmetries
KW - Relativistic spin
KW - Theories with constraints
KW - Zitterbewegung
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UR - http://www.scopus.com/inward/citedby.url?scp=84855549517&partnerID=8YFLogxK
U2 - 10.1016/j.aop.2011.11.019
DO - 10.1016/j.aop.2011.11.019
M3 - Article
AN - SCOPUS:84855549517
VL - 327
SP - 398
EP - 406
JO - Annals of Physics
JF - Annals of Physics
SN - 0003-4916
IS - 2
ER -