Vector and Axial anomaly in the Thirring-Wess model

TL;DR

This paper rigorously analyzes the 2D Thirring-Wess model, demonstrating the presence of the Adler-Bell-Jackiw anomaly and its effects on correlation functions, with implications for quantum field theory and anomaly physics.

Contribution

It provides a rigorous proof of the axial and vector anomaly effects in the Thirring-Wess model using a renormalization group approach, confirming key theoretical predictions.

Findings

The meson-meson correlation matches a free boson propagator with mass renormalization.

The anomaly is quadratic in the charge, consistent with the Adler-Bardeen formula.

Fermion-fermion correlation exhibits anomalous long-distance decay.

Abstract

We study the 2D Vector Meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization group approach, that the vector and axial Ward identities are broken by the Adler-Bell-Jackiw anomaly; and we rigorously establish three widely believed consequences: a) the interacting meson-meson correlation equals a free boson propagator, though the mass is additively renormalized by the anomaly; b) the anomaly is quadratic in the charge, in agreement with the Adler-Bardeen formula; c) the fermion-fermion correlation has an anomalous long-distance decay.