On the developments of Sklyanin's quantum separation of variables for integrable quantum field theories

TL;DR

This paper advances Sklyanin's quantum separation of variables (SOV) method for solving 1+1-dimensional integrable quantum field theories, exemplified by the sine-Gordon model, enabling spectrum and dynamics analysis.

Contribution

It introduces a new method within the SOV framework to derive spectra and correlation functions for integrable quantum field theories.

Findings

Spectrum and eigenstates derived for sine-Gordon model

Method applicable to a broader class of models

Complete characterization of the spectrum achieved

Abstract

We present a microscopic approach in the framework of Sklyanin's quantum separation of variables (SOV) for the exact solution of 1+1-dimensional quantum field theories by integrable lattice regularizations. Sklyanin's SOV is the natural quantum analogue of the classical method of separation of variables and it allows a more symmetric description of classical and quantum integrability w.r.t. traditional Bethe ansatz methods. Moreover, it has the advantage to be applicable to a more general class of models for which its implementation gives a characterization of the spectrum complete by construction. Our aim is to introduce a method in this framework which allows at once to derive the spectrum (eigenvalues and eigenvectors) and the dynamics (time dependent correlation functions) of integrable quantum field theories (IQFTs). This approach is presented for a paradigmatic example of relativistic IQFT, the sine-Gordon model.