Towards the Construction of Wightman Functions of Integrable Quantum Field Theories

TL;DR

This paper explores the explicit construction of Wightman functions in integrable 1+1 dimensional quantum field theories, focusing on sine-Gordon, sinh-Gordon, and scaling Ising models, advancing the bootstrap approach.

Contribution

It demonstrates the explicit construction of Wightman functions for integrable models using the bootstrap program, including summation over intermediate states in short distance limits.

Findings

Explicit Wightman functions constructed for sine-Gordon and sinh-Gordon models.

Summation over intermediate states achieved in short distance limit.

Review of form factors and operator equations in integrable models.

Abstract

The purpose of the ``bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, this program is mainly illustrated in terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.