Beyond Symmetries : Anomalies in Transverse Ward--Takahashi Identities

TL;DR

This paper investigates the existence and properties of transverse anomalies in Ward--Takahashi identities using Fujikawa's method and dimensional renormalization, revealing their arbitrary coefficients and discussing their physical implications.

Contribution

It provides a rigorous analysis of transverse anomalies at all loop orders and clarifies their relation to Schwinger terms and other anomalies, challenging previous claims of their non-existence.

Findings

Transverse anomalies exist at one-loop and all loop orders.

Coefficients of transverse anomalies are arbitrary.

A proposed resolution relates transverse anomalies to Schwinger terms.

Abstract

Anomalies in transverse Ward--Takahashi identities are studied, allowing discussion of the feasibility of anomalies arising in general non-symmetry Ward--Takahashi identities. We adopt the popular Fujikawa's method and rigorous dimensional renormalization to verify the existence of transverse anomalies to one-loop order and any loop order, respectively. The arbitrariness of coefficients of transverse anomalies is revealed, and a way out is also proposed after relating transverse anomalies to Schwinger terms and comparing symmetry and non-symmetry anomalies. Papers that claim the non-existence of transverse anomalies are reviewed to find anomalies hidden in their approaches. The role played by transverse anomalies is discussed.