Classical description of spinning degrees of freedom of relativistic particles by means of commuting spinors

Citation
Aa. Deriglazov et Dm. Gitman, Classical description of spinning degrees of freedom of relativistic particles by means of commuting spinors, MOD PHY L A, 14(10-11), 1999, pp. 709-720
Citations number
43
Categorie Soggetti
Physics
Journal title
MODERN PHYSICS LETTERS A
ISSN journal
02177323 → ACNP
Volume
14
Issue
10-11
Year of publication
1999
Pages
709 - 720
Database
ISI
SICI code
0217-7323(19990410)14:10-11<709:CDOSDO>2.0.ZU;2-Q
Abstract
We consider a possibility of describing spin one-half and higher spins of m assive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables x(mu), xi(alpha), chi(alpha), wh ere xi, chi are commuting Majorana spinors. In the course of quantization b oth models reproduce Dirac equation. We analyze the possibility of introduc ing an interaction with an external electromagnetic background into the mod els and generalizing them to higher spin description. The first model admit s a minimal interaction with the external electromagnetic field, but leads to reducible representations of the Poincare group being generalized for hi gher spins. The second model turns out to be appropriate for description of the massive higher spins. However, it seems to be difficult to introduce a minimal interaction with an external electromagnetic field into this model . We compare our approach with one, which uses Grassmann variables, and est ablish a relation between them.