The Bethe Ansatz and the Tzitz\'eica-Bullough-Dodd equation

TL;DR

This paper explores the mathematical connection between classical integrable nonlinear wave equations and quantum Bethe Ansatz systems, focusing on the Tzitzéica-Bullough-Dodd model, and discusses its physical interpretation.

Contribution

It establishes a detailed correspondence between classical and quantum versions of the Tzitzéica-Bullough-Dodd model, advancing understanding of their mathematical and physical relationship.

Findings

Identifies a mathematical link between classical and quantum models.

Provides insights into the physical interpretation of the Bethe Ansatz correspondence.

Enhances the theoretical framework for integrable quantum field theories.

Abstract

The theory of classically integrable nonlinear wave equations, and the Bethe Ansatz systems describing massive quantum field theories defined on an infinite cylinder, are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper we shall describe this link for the case of the classical and quantum versions of the (Tzitz\'eica-)Bullough-Dodd model.