A new interpretation of Bethe ansatz solutions for massive Thirring model

TL;DR

This paper reanalyzes Bethe ansatz solutions for the massive Thirring model, revealing a single bound state and scattering states with real rapidities, aligning with previous infinite momentum frame results.

Contribution

It provides a numerical solution to Bethe ansatz equations without density of states assumptions, identifying the bound state spectrum and ruling out string-like solutions.

Findings

Only one bound state exists in the model.

No string-like solutions are found.

Boson-boson scattering states have real rapidities.

Abstract

We reexamine Bethe ansatz solutions of the massive Thirring model. We solve equations of periodic boundary conditions numerically without referring to the density of states. It is found that there is only one bound state in the massive Thirring model. The bound state spectrum obtained here is consistent with Fujita-Ogura's solutions of the infinite momentum frame prescription. Further, it turns out that there exist no solutions for string-like configurations. Instead, we find boson boson scattering states in 2-particle 2-hole configurations where all the rapidity variables turn out to be real.