Path integral and pseudoclassical action for spinning particle in external electromagnetic and torsion fields

We study a possibility for pseudoclassical description of a spinning particle in external electromagnetic and torsion fields. To this end we depart from the Dirac equation in such a background and derive a path integral representation for the corresponding propagator. An effective action which appears in the representation is interpreted as a pseudoclassical action for the spinning particle. It is a generalization of Berezin-Marinov action to the background under consideration. Pseudoclassical equations of motion in the nonrelativistic limit reproduce exactly the classical limit of the Pauli quantum mechanics in the same case. Quantization of the action appears to be nontrivial due to e-mail: [email protected] On leave from Instituto de Fisica, University of São Paulo, Brasil; e-mail: [email protected] On leave from Tomsk Pedagogical University, Russia; e-mail: [email protected]