Topological index associated with transverse axial vector and vector anomalies in QED

TL;DR

This paper introduces a new topological index linked to a novel anomaly in QED, arising from the transverse Ward-Takahashi identity for pseudo-tensor currents, connecting quantum anomalies with topological invariants.

Contribution

It identifies a previously unknown anomaly in QED related to transverse Ward-Takahashi identity and relates it to the Atiyah-Singer index theorem, establishing a topological index.

Findings

Discovery of a novel anomaly in QED

Connection between the anomaly and the Atiyah-Singer index theorem

Introduction of a topological index associated with the anomaly

Abstract

It is shown that a novel anomaly associated with transverse Ward-Takahashi identity exists for pseudo-tensor current in QED, and the anomaly gives rise to a topological index of Dirac operator in terms of Atiyah-Singer index theorem.