Functional Integral Construction of the Thirring model: axioms verification and massless limit

TL;DR

This paper constructs a rigorous quantum field theory for the Thirring model using functional integrals, verifying axioms and analyzing anomalies in Ward identities and propagator equations.

Contribution

It provides a novel functional integral construction of the Thirring model for any mass, verifying axioms and exploring anomaly structures.

Findings

Convergence of Grassmann integrals as cutoffs are removed

Verification of Osterwalder-Schrader axioms for the constructed model

Identification of non-linear anomalies in Ward identities

Abstract

We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader axioms. The corresponding Ward Identities have anomalies which are not linear in the coupling and which violate the anomaly non-renormalization property. Additional anomalies are present in the closed equation for the interacting propagator, obtained by combining a Schwinger-Dyson equation with Ward Identities.