Lectures on S-matrices and Integrability

TL;DR

This paper reviews the theory of S-matrices in (1+1)-dimensional integrable models, emphasizing their properties, factorization, and specific models like sine-Gordon and chiral Gross-Neveu, providing foundational insights for researchers.

Contribution

It offers a comprehensive review of S-matrix theory in integrable models, including derivations, algebraic structures, and applications to specific models, with pedagogical focus.

Findings

Derivation of S-matrices for bound states using bootstrap principle

Analysis of analytic properties of two-particle scattering amplitudes

Discussion of algebraic structures and model-specific S-matrices

Abstract

In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU(2), SU(3) chiral Gross-Neveu models. This is part of a collection of lecture notes for the Young Researchers Integrability School, organized by the GATIS network at Durham University on 6-10 July 2015.