Wedge-local fields in integrable models with bound states

TL;DR

This paper extends the construction of wedge-local observables in 2D integrable quantum field theories to include models with bound states, characterized by S-matrices with poles in the physical strip, advancing the operator-algebraic approach.

Contribution

It introduces a method to construct wedge-local observables for scalar factorizing S-matrices with poles, broadening the class of models beyond analytic S-matrices.

Findings

Constructed candidate wedge-local observables with poles in the physical strip.

Showed these operators weakly commute on a certain domain.

Discussed technical issues related to self-adjointness and strong commutativity.

Abstract

Recently, large families of two-dimensional quantum field theories with factorizing S-matrices have been constructed by the operator-algebraic methods, by first showing the existence of observables localized in wedge-shaped regions. However, these constructions have been limited to the class of S-matrices whose components are analytic in rapidity in the physical strip. In this work, we construct candidates for observables in wedges for scalar factorizing S-matrices with poles in the physical strip and show that they weakly commute on a certain domain. We discuss some technical issues concerning further developments, especially the self-adjointness of the candidate operators here and strong commutativity between them.