A Classical Version of the Non-Abelian Gauge Anomaly

TL;DR

This paper demonstrates that a classical Hamiltonian flow approach, incorporating Berry phase effects, can reproduce the covariant gauge anomaly for chiral fermions in non-Abelian gauge theories, bridging classical and quantum perspectives.

Contribution

It introduces a classical Hamiltonian framework that captures the non-Abelian gauge anomaly using Berry phase, offering a new perspective on anomaly derivation.

Findings

Classical Hamiltonian flow reproduces gauge anomaly.

Berry phase is essential for anomaly emergence.

Bridges classical and quantum descriptions of anomalies.

Abstract

We show that a version of the covariant gauge anomaly for a 3+1 dimensional chiral fermion interacting with a non-Abelian gauge field can be obtained from the classical Hamiltonian flow of its probability distribution in phase space. The only quantum input needed is the Berry phase that arises from the direction of the spin being slaved to the particle's momentum.