Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory

TL;DR

This paper establishes a connection between matrix elements in integrable models solved by the Algebraic Bethe Ansatz and form factors in relativistic quantum field theories, enabling easier computations of these elements.

Contribution

It demonstrates that Bethe Ansatz matrix elements can be obtained as non-relativistic limits of relativistic form factors, providing a new computational approach.

Findings

Matrix elements correspond to non-relativistic limits of form factors.

The method simplifies calculations of Bethe Ansatz matrix elements.

Application shown for Quantum Non-Linear Schrödinger and Sinh-Gordon models.

Abstract

We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compute matrix elements of Bethe Ansatz integrable models, overpassing the technical difficulties of their direct determination. We analyze this correspondence for the simplest example in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon models.