Pseudoclassical Foldy-Wouthuysen transformation and the canonical quantization of the D=2n dimensional spinning particle in the external electromagnetic field

TL;DR

This paper develops a canonical quantization method for D=2n dimensional Dirac spinning particles in external electromagnetic fields, using a pseudoclassical Foldy-Wouthuysen transformation to obtain Newton-Wigner coordinates and connect with existing Dirac particle models.

Contribution

It introduces a novel approach combining pseudoclassical Foldy-Wouthuysen transformation with canonical quantization for higher-dimensional Dirac particles in electromagnetic fields.

Findings

Successful derivation of canonical coordinates for D=2n dimensional Dirac particles.

Establishment of a link between the quantization method and the Blount picture.

Framework for describing particles and antiparticles at the classical level.

Abstract

The canonical quantization of $D=2n$ dimensional Dirac spinning particle 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 Blount picture of Dirac particle in the external electromagnetic field is discussed.