Self-adjointness of bound state operators in integrable quantum field theory

TL;DR

This paper investigates the self-adjoint extensions of certain operators in integrable quantum field theory, crucial for modeling bound states of particles and constructing algebraic frameworks of these theories.

Contribution

It computes deficiency indices for a broad class of operators and identifies conditions for self-adjoint extensions related to analytic continuation in quantum field models.

Findings

Computed deficiency indices for a wide class of operators.

Identified a self-adjoint extension unitarily equivalent to analytic continuation.

Provided mathematical foundation for constructing quantum field theory models with bound states.

Abstract

We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class of analytic functions. For functions of a particular form, we point out the existence of a self-adjoint extension which is unitarily equivalent to the analytic-continuation operation. They appear in integrable quantum field theories as the one-particle component of the operators which realize the bound states of elementary particles and the existence of self-adjoint extension is a necessary step for the construction of Haag-Kastler net for such models.