Path Integrals and Pseudoclassical Description for Spinning Particles in Arbitrary Dimensions

TL;DR

This paper develops a path integral formulation for spinning particles in arbitrary dimensions, introducing a new pseudoclassical action for odd dimensions and demonstrating its consistency with quantum theory.

Contribution

It provides the first solution for the propagator of spinning particles in odd dimensions and proposes a new gauge invariant action suitable for quantization in these cases.

Findings

New pseudoclassical action for odd dimensions

Operator quantization yields consistent quantum theory

Generalization to particles with anomalous magnetic moment

Abstract

The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is just a generalization of one in four dimensions (it has been known before). In this case a gauge invariant part of the effective action in the path integral has a form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs from the standard one. We propose this new action as a candidate to describe spinning particles in odd dimensions. Studying the hamiltonization of the pseudoclassical theory with this action, we show that the operator quantization leads to adequate minimal quantum theory of spinning particles in odd dimensions. In contrast with the models proposed formerly in this case the new one admits both the operator and the path integral quantization. Finally the consideration is generalized for the case of the particle with anomalous magnetic moment.