Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. I

摘要

The problem on mapping between two Lagrangian descriptions (using a commuting c-number spinor psi(alpha) or anticommuting pseudovector xi(mu)and pseudoscalar xi(5) variables) of the spin degrees of freedom of a color spinning massive particle interacting with background non-Abelian gauge field, is considered. A general analysis of the mapping between a pair of Majorana spinors (psi(alpha), theta(alpha)) (theta(alpha) is some auxiliary anticommuting spinor) and a real anticommuting tensor aggregate (S, V-mu, *T-mu nu, A(mu), P), is presented. A complete system of bilinear relations between the tensor quantities, is obtained. The analysis we have given is used for the above problem of the equivalence of two different ways of describing the spin degrees of freedom of the relativistic particle. The mapping of the kinetic term (i (h) over bar /2)((theta) over bar theta)((psi) over bar psi - (psi) over bar(psi)over dot), the term (1/e)((theta) over bar theta)(x)over dot(mu)((psi) over bar gamma(mu)psi) that provides a couple of the spinning variable psi and the particle velocity (x)over dot(mu), and the interaction term (h) over bar((theta) over bar theta)Q(a)F(mu nu)(a)((psi) over bar sigma(mu nu)psi) with an external non-Abelian gauge field, are considered in detail. In the former case a corresponding system of bilinear identities including both the tensor variables and their derivatives ((S)over dot, (V)over dot(mu), *(T)over dot(mu nu), (A)over dot(mu), (P)over dot), is defined. A detailed analysis of the local bosonic synunetry of the Lagrangian with the commuting spinor psi(alpha), is carried out. A connection of this symmetry with the local SUSY transformation of the Lagrangian containing anticommuting pseudovector and pseudoscalar variables, is considered. The approach of obtaining a supersymmetric Lagrang,ian in terms of the even psi(alpha) and odd theta(alpha) spinors, is offered. (C) 2015 Elsevier B.V. All rights reserved.