### Abstract

We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both Γμ and Γμν-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.

Original language | English |
---|---|

Article number | 122303 |

Journal | Journal of Mathematical Physics |

Volume | 53 |

Issue number | 12 |

DOIs | |

Publication status | Published - 19 Dec 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*53*(12), [122303]. https://doi.org/10.1063/1.4759500

**Non-Grassmann mechanical model of the Dirac equation.** / Deriglazov, A. A.; Rizzuti, B. F.; Zamudio, G. P.; Castro, P. S.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 53, no. 12, 122303. https://doi.org/10.1063/1.4759500

}

TY - JOUR

T1 - Non-Grassmann mechanical model of the Dirac equation

AU - Deriglazov, A. A.

AU - Rizzuti, B. F.

AU - Zamudio, G. P.

AU - Castro, P. S.

PY - 2012/12/19

Y1 - 2012/12/19

N2 - We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both Γμ and Γμν-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.

AB - We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both Γμ and Γμν-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.

UR - http://www.scopus.com/inward/record.url?scp=84871997941&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871997941&partnerID=8YFLogxK

U2 - 10.1063/1.4759500

DO - 10.1063/1.4759500

M3 - Article

AN - SCOPUS:84871997941

VL - 53

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

M1 - 122303

ER -