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

TL;DR

This paper derives a path integral representation for a spinning particle in electromagnetic and torsion fields, generalizing the Berezin-Marinov action, and connects it to the Dirac equation in such backgrounds.

Contribution

It introduces a generalized pseudoclassical action for spinning particles in complex backgrounds and discusses its quantization and relation to the Dirac equation.

Findings

Path integral representation for the propagator in external fields.

Generalization of Berezin-Marinov action to include torsion fields.

Quantization reproduces the Dirac equation in the specified background.

Abstract

Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a pseudoclassical action for a spinning particle. It is just 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 an ordering problem, which needs to be solved to construct operators of first-class constraints, and to select the physical sector. Finally the quantization reproduces the Dirac equation in the given background and, thus, justifies the interpretation of the action.