Classical chiral kinetic theory and anomalies in even space-time dimensions

TL;DR

This paper develops a classical action framework for massless Weyl fermions in even-dimensional spacetime, deriving a Boltzmann equation and illustrating how classical gauge and chiral anomalies emerge from Berry curvature effects.

Contribution

It introduces a classical action for Weyl fermions in even-dimensional spacetime and connects anomalies to Berry curvature, bridging classical kinetic theory and quantum anomalies.

Findings

Derived collisionless Boltzmann equation for Weyl fermions.

Showed classical anomalies originate from Berry curvature.

Connected gauge anomalies to topological properties of Berry connection.

Abstract

We propose a classical action for the motion of massless Weyl fermions in a background gauge field in (2N+1)+1 spacetime dimensions. We use this action to derive the collisionless Boltzmann equation for a gas of such particles, and show how classical versions of the gauge and Abelian chiral anomalies arise from the Chern character of the non-Abelian Berry connection that parallel transports the spin degree of freedom in momentum space.