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
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.