Pseudoclassical and quantum theory of the D=2n dimensional relativistic spinning particle with anomalous "magnetic" moment in the external Yang-Mills field

TL;DR

This paper develops a pseudoclassical and quantum framework for a D=2n dimensional Dirac spinning particle with anomalous magnetic moment interacting with Yang-Mills fields, including classical equations of motion and quantization methods.

Contribution

It introduces a comprehensive pseudoclassical Hamiltonian, derives equations of motion, and performs canonical quantization for the Dirac particle with anomalous magnetic moment in higher dimensions.

Findings

Derived the pseudoclassical Hamiltonian and action.

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

Performed canonical quantization in a gauge accommodating particles and antiparticles.

Abstract

The pseudoclassical hamiltonian and action of the $D=2n$ dimensional Dirac particle with anomalous magnetic moment interacting with the external Yang-Mills field are 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 Yang-Mills 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 these variables the theory is quantized.