Non-Grassmann mechanical model of the Dirac equation

A. A. Deriglazov, B. F. Rizzuti, G. P. Zamudio, P. S. Castro

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Article number122303
JournalJournal of Mathematical Physics
Volume53
Issue number12
DOIs
Publication statusPublished - 19 Dec 2012
Externally publishedYes

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Dirac Equation
Dirac equation
Quantization
Orbit
de Broglie wavelengths
orbits
Anti-de Sitter Space
Hamiltonian Formulation
Barycentre
General Solution
Model
confining
metal spinning
center of mass
Equations of Motion
equations of motion
degrees of freedom
Space-time
Degree of freedom
Wavelength

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Deriglazov, A. A., Rizzuti, B. F., Zamudio, G. P., & Castro, P. S. (2012). Non-Grassmann mechanical model of the Dirac equation. 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.

In: Journal of Mathematical Physics, Vol. 53, No. 12, 122303, 19.12.2012.

Research output: Contribution to journalArticle

Deriglazov, AA, Rizzuti, BF, Zamudio, GP & Castro, PS 2012, 'Non-Grassmann mechanical model of the Dirac equation', Journal of Mathematical Physics, vol. 53, no. 12, 122303. https://doi.org/10.1063/1.4759500
Deriglazov AA, Rizzuti BF, Zamudio GP, Castro PS. Non-Grassmann mechanical model of the Dirac equation. Journal of Mathematical Physics. 2012 Dec 19;53(12). 122303. https://doi.org/10.1063/1.4759500
Deriglazov, A. A. ; Rizzuti, B. F. ; Zamudio, G. P. ; Castro, P. S. / Non-Grassmann mechanical model of the Dirac equation. In: Journal of Mathematical Physics. 2012 ; Vol. 53, No. 12.
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