The Quantum Sine Gordon model in perturbative AQFT

TL;DR

This paper investigates the quantum Sine-Gordon model within perturbative algebraic quantum field theory, demonstrating convergence of key formal series and analyzing the vertex operator algebra braiding property.

Contribution

It provides the first rigorous proof of convergence for the Epstein Glaser S-matrix and interacting fields in the finite regime of the Sine-Gordon model.

Findings

Convergence of the Epstein Glaser S-matrix in the finite regime.

Verification of the braiding property of vertex operator algebra.

Formal power series for the interacting current and field converge.

Abstract

We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation value - with respect to the vacuum or a Hadamard state - of the Epstein Glaser S-matrix and the interacting current or the field respectively, both given as formal power series, converge.