On Form Factors of the conjugated field in the non-linear Schr\"oodinger model

TL;DR

This paper proves the convergence of lattice form factors to continuous model form factors in the non-linear Schrödinger model and analyzes their large-volume asymptotics using Fredholm determinants.

Contribution

It demonstrates the zero lattice spacing limit of lattice form factors and introduces a method to define Fredholm determinants for general parameters.

Findings

Form factors converge to continuous model results in the zero lattice spacing limit.

Large-volume asymptotics characterized by Fredholm determinants.

Method to define Fredholm determinants for generic parameters.

Abstract

Izergin-Korepin's lattice discretization of the non-linear Schr\"odinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic parameters.