PATH-INTEGRALS AND PSEUDOCLASSICAL DESCRIPTION FOR SPINNING PARTICLESIN ARBITRARY DIMENSIONS

The propagator of a spinning particle in an external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even di mensions the representation is just a generalization of the one in fou r dimensions (which is already known), In this case the gauge invarian t part of the effective action in the path integral has the form of th e standard (Berezin-Marinov) pseudoclassical action, In odd dimensions the solution is presented for the first time and, in particular, it t urns out that the gauge invariant part of the effective action differs from the standard one, We propose this new action as a candidate to d escribe spinning particles in odd dimensions, Studying the Hamiltoniza tion of the pseudoclassical theory with the new action we show that th e operator quantization leads to an adequate minimal quantum theory of spinning particles in odd dimensions, Finally the consideration is ge neralized for the case of a particle with an anomalous magnetic moment .