Wightman axiomatics of the bootstrap construction of the 1+1 dimensional Sinh-Gordon model

TL;DR

This paper demonstrates that, assuming the convergence of series, the bootstrap construction of the 1+1 dimensional Sinh-Gordon model satisfies all Wightman axioms, supporting its validity as a quantum field theory.

Contribution

It provides a Wightman axiomatics framework for the bootstrap construction of the Sinh-Gordon model, contingent on the convergence of the series involved.

Findings

Expressions satisfy all Wightman axioms assuming convergence.

Supports the bootstrap approach as a valid construction of quantum field theory.

Highlights the open problem of proving series convergence.

Abstract

The integrable bootstrap program allows one to express the tempered distributions associated with the multipoint functions of the integrable 1+1 dimensional Sinh-Gordon quantum field theory by means of explicit series. The convergence of the latter is an open problem that was only solved for the two-point case. In this work, by taking for granted the convergence of these series, we show that these expressions satisfy all of the Wightman axioms. This thus shows that, upon a yet to be proven convergence property, the integrable bootstrap based construction of correlation functions does lead to a quantum field theory.