Quantization of Spinning Particle with Anomalous Magnetic Momentum

TL;DR

This paper develops a generalized action for a spinning particle with an anomalous magnetic moment, exploring its quantization via operator and path-integral methods, and addressing operator ordering issues for consistency.

Contribution

It introduces a reparametrization and supergauge invariant action for a spinning particle with anomalous magnetic moment derived from path integral methods, and compares quantization schemes.

Findings

Derivation of a generalized pseudoclassical action for particles with anomalous magnetic moments.

Analysis of Dirac and BFV quantization schemes and their implications.

Identification of operator ordering issues necessary for consistent quantization.

Abstract

A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic moment is given. The leading considerations, to write the action, are gotten from the path integral representation for the causal Green's function of the generalized (by Pauli) Dirac equation for the particle with anomalous magnetic momentum in an external electromagnetic field. The action can be written in reparametrization and supergauge invariant form. Both operator (Dirac) and path-integral (BFV) quantization are discussed. The first one leads to the Dirac-Pauli equation, whereas the second one gives the corresponding propagator. One of the nontrivial points in this case is that both quantizations schemes demand for consistency to take into account an operators ordering problem.