Cancellation of anomalies in a path integral formulation for classical field theories

TL;DR

This paper demonstrates that classical field theories formulated via path integrals can cancel quantum anomalies by including auxiliary fields, restoring symmetries that are broken during quantization.

Contribution

It introduces a path integral formulation for classical field theories that includes auxiliary fields to cancel quantum anomalies and restore symmetries.

Findings

Auxiliary fields transform to cancel Jacobian factors

Quantum anomalies are canceled at the classical level

Symmetries broken during quantization can be restored classically

Abstract

Some symmetries can be broken in the quantization process (anomalies) and this breaking is signalled by a non-invariance of the quantum path integral measure. In this talk we show that it is possible to formulate also classical field theories via path integral techniques. The associated classical functional measure is larger than the quantum one, because it includes some auxiliary fields. For a fermion coupled with a gauge field we prove that the way these auxiliary fields transform compensates exactly the Jacobian which arises from the transformation of the fields appearing in the quantum measure. This cancels the quantum anomaly and restores the symmetry at the classical level.