Pseudoclassical Model of Spinning Particle with Anomalous Magnetic Momentum

TL;DR

This paper develops a pseudoclassical model for a spinning particle with an anomalous magnetic moment, leading to a consistent Dirac quantization that results in the Dirac-Pauli equation in an external electromagnetic field.

Contribution

It introduces a generalized, gauge-invariant pseudoclassical action for spinning particles with anomalous magnetic moments, addressing operator ordering issues during quantization.

Findings

Derivation of the Dirac-Pauli equation from the model

Identification of operator ordering problems in quantization

Establishment of a gauge-invariant pseudoclassical framework

Abstract

A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic momentum is given. The action is written in reparametrization and supergauge invariant form. The Dirac quantization, based on the Hamiltonian analyses of the model, leads to the Dirac-Pauli equation for a particle with an anomalous magnetic momentum in an external electromagnetic field. Due to the structure of first-class constraints in that case, the Dirac quantization demands for consistency to take into account an operators ordering problem.