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

We propose a classical action for the motion of massless Weyl fermions in a background gauge field in (2N + 1) + 1 space-time 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.