Anomalies and Bose symmetry

TL;DR

This paper discusses how Bose symmetry in triangle diagrams for chiral currents is not manifest and introduces a way to resolve the ambiguity, leading to the derivation of the Adler-Bell-Jackiw anomaly.

Contribution

It highlights the role of Bose symmetry in fixing momentum-routing ambiguity in triangle diagrams, providing insight into the origin of the chiral anomaly.

Findings

Bose symmetry is not manifest in the triangle diagram for chiral currents.

Imposing Bose symmetry resolves the momentum-routing ambiguity.

This leads to the derivation of the Adler-Bell-Jackiw anomaly.

Abstract

We point out a feature of the triangle diagram for three chiral currents which is perhaps not widely appreciated: Bose symmetry is not manifest and suffers from a momentum-routing ambiguity. Imposing Bose symmetry fixes the ambiguity and leads to the famous Adler - Bell - Jackiw anomaly.