Quantisation without Witten Anomalies

TL;DR

This paper demonstrates that gauge anomalies can be eliminated by considering Berry's phase and boundary conditions in the path integral, avoiding the need for extra quantum fields to cancel anomalies.

Contribution

It introduces a method to remove gauge anomalies through Berry's phase considerations, challenging the necessity of additional fields in anomalous gauge theories.

Findings

Gauge anomalies are artifacts of quantum field theory under certain conditions.

Berry's phase can eliminate gauge anomalies associated with nontrivial gauge transformations.

No extra quantum fields are needed to cancel anomalies in this approach.

Abstract

It is argued that the gauge anomalies are only the artefacts of quantum field theory when certain subtleties are not taken into account. With the Berry's phase needed to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are shown explicitly to be eliminated, without any extra quantum fields introduced. This is in contra-distinction to other quantisations of `anomalous' gauge theory where extra, new fields are introduced to explicitly cancel the anomalies.