Free energy from forward scattering in 1+1d

TL;DR

This paper explores how to accurately compute the ground state energy in 1+1 dimensional quantum field theories using forward scattering amplitudes, addressing singularities and including bound states, with applications to several models.

Contribution

It demonstrates a method to apply the forward scattering approach to multi-particle scattering in 1+1d theories, including non-integrable models and bound states, improving upon naive treatments.

Findings

Validated the approach against exact results for various models

Extended the method to include bound states in attractive models

Resolved singularities in multi-particle scattering calculations

Abstract

The free energy, or equivalently the ground state energy in finite volume, may be calculated from forward scattering amplitudes using a formula due to Dashen, Ma, and Bernstein. However a naive treatment leads to singularities when considering the scattering of three or more particles. It is shown in detail how the approach can be applied to multi-particle scattering in various massive scalar theories in 1+1d, with or without integrability. The results for the sinh-Gordon, Lieb-Liniger, and $O(N)$ non-linear sigma models are compared to exact results. It is shown how bound states can be considered in this approach by considering the attractive Lieb-Liniger model.