Correspondence between classical and pseudoclassical descriptions of the spin degree of freedom of a relativistic particle in an external field

摘要

A generalization of the Lagrangian description of a relativistic color charged spinning particle interacting with external non-Abelian gauge and fermion fields, previously introduced by the authors, is proposed which takes into account the time-varying spin degree of freedom of the particle. For the case under consideration, the degree of freedom is described by a classical commuting Dirac spinor ψα. This spinor has been mapped to new (anticommuting) variables: a pseudovector ξ_μ, a pseudoscalar ξ_5, a pseudotensor *ζ_(μν), a vector ξ?_μ,and a scalar ξ?_5. The first two of them are usually used in a pseudoclassical description of the spin degree of freedom of a massive spin 1/2 particle. The mapping (ψ_α, ψ?_α has been examined for oneoneness. It has been shown that to attain one-oneness, it is necessary either to narrow the class of the initial spinor ψ_α to that of Majorana particles or to double the number of variables in the set of tensors (ξ_μ, ξ_5, *ζ_(μν), ξ?_μ, ξ?_5).