Local nets of von Neumann algebras in the Sine-Gordon model

TL;DR

This paper constructs a local net of von Neumann algebras for the sine-Gordon model in the ultraviolet finite regime, proving its equivalence with the massive Thirring model without auxiliary mass terms, using Lorentzian signature methods.

Contribution

It provides a Lorentzian signature construction of the sine-Gordon model's local algebras and establishes their equivalence with the massive Thirring model, extending previous work.

Findings

Construction of local von Neumann algebras for sine-Gordon model

Proof of equivalence with massive Thirring model

Work done entirely in Lorentzian signature without auxiliary mass

Abstract

The Haag-Kastler net of local von Neumann algebras is constructed in the ultraviolet finite regime of the sine-Gordon model, and its equivalence with the massive Thirring model is proved. In contrast to other authors, we do not add an auxiliary mass term, and we work completely in Lorentzian signature. The construction is based on the functional formalism for perturbative Algebraic Quantum Field Theory together with estimates originally derived within Constructive Quantum Field Theory and adapted to Lorentzian signature. The paper extends previous work by two of us.