A Semiclassical Kinetic Theory of Dirac Particles and Thomas Precession

TL;DR

This paper develops a semiclassical kinetic theory for Dirac particles using matrix valued differential forms, incorporating Thomas precession and Berry gauge fields to improve understanding of Dirac fermion dynamics.

Contribution

It introduces a new approach to Dirac fermion kinetic theory that naturally includes Thomas precession and clarifies the role of Berry gauge fields in equations of motion.

Findings

Thomas precession correction can be incorporated straightforwardly

Thomas precession cancels Berry gauge field terms in equations of motion

Method works in the helicity basis for massless limit

Abstract

Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields.