# Derivation of Semiclassical Kinetic Theory in the Presence of Non-Abelian Berry Curvature

## TL;DR

This paper derives semiclassical kinetic equations incorporating non-Abelian Berry curvature effects for particles in degenerate energy bands, using phase-space quantum mechanics to systematically account for fictitious forces.

## Contribution

It provides a systematic derivation of Boltzmann equations with non-Abelian Berry curvature effects in degenerate bands, advancing semiclassical theory.

## Key findings

- Derived kinetic equations with non-Abelian Berry curvature
- Systematic use of phase-space quantum mechanics
- Clarified effects of Berry curvature on particle dynamics

## Abstract

In quantum mechanics it is often required to describe in a semiclassical approximation the motion of particles moving within a given energy band. Such a representation leads to the appearance of an analogues of fictitious forces in the semiclassical equations of motion associated with the Berry curvature. The purpose of this paper is to derive systematically the kinetic Boltzmann equations displaying these effects in the case that the band is degenerate, and as such the Berry curvature is non-Abelian. We use the formalism of phase-space quantum mechanics to derive the results.