Inverse Scattering and Locality in Integrable Quantum Field Theories

TL;DR

This paper develops a method to reconstruct integrable quantum field theories from their scattering data, accommodating complex gauge symmetries and broad classes of S-matrices, advancing the mathematical understanding of these models.

Contribution

It introduces a generalized solution method for the inverse scattering problem in integrable quantum field theories with non-scalar particles and gauge symmetries, extending previous scalar-focused approaches.

Findings

Criteria for S-matrices ensuring inverse scattering solutions

Application to diagonal and $O(N)$-invariant models

Use of operator algebras and complex analysis techniques

Abstract

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix $S$ is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on $S$ that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the $O(N)$-invariant nonlinear $\sigma$-models.