### 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 |
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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 |

### Fingerprint

### Keywords

- Dirac equation
- Local (gauge) symmetries
- Relativistic spin
- Theories with constraints
- Zitterbewegung

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*327*(2), 398-406. https://doi.org/10.1016/j.aop.2011.11.019

**A semiclassical description of relativistic spin without the use of Grassmann variables and the Dirac equation.** / Deriglazov, A. A.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 327, no. 2, pp. 398-406. https://doi.org/10.1016/j.aop.2011.11.019

}

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

UR - http://www.scopus.com/inward/record.url?scp=84855549517&partnerID=8YFLogxK

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 -