Canonical quantization of the D=2n dimensional relativistic spinning particle with anomalous magnetic moment in the external electromagnetic field

TL;DR

This paper develops a canonical quantization framework for the D=2n dimensional Dirac spinning particle with anomalous magnetic moment in an external electromagnetic field, deriving equations of motion and connecting classical and quantum descriptions.

Contribution

It introduces a pseudoclassical Hamiltonian and action for the Dirac particle with anomalous magnetic moment in higher dimensions, and performs a canonical quantization using Foldy-Wouthuysen transformation.

Findings

Derived the Bargmann-Michel-Telegdi equation for the Pauli-Lubanski vector.

Achieved a quantization scheme that describes particles and antiparticles at the classical level.

Connected the quantization with existing descriptions of Dirac particles with anomalous magnetic moments.

Abstract

The pseudoclassical hamiltonian and action of the $D=2n$ dimensional Dirac particle with anomalous magnetic moment interacting with the external electromagnetic field is found. The Bargmann-Michel-Telegdi equation of motion for the Pauli-Lubanski vector is deduced. The canonical quantization of $D=2n$ dimensional Dirac spinning particle with anomalous magnetic moment in the external electromagnetic field is carried out in the gauge which allows to describe simultaneously particles and antiparticles (massive and massless) already at the classical level. Pseudoclassical Foldy-Wouthuysen transformation is used to obtain canonical (Newton-Wigner) coordinates and in terms of this variables the theory is quantized. The connection of this quantization with the deGroot and Suttorp's description of Dirac particle with anomalous magnetic moment in the external electromagnetic field is discussed.