Bound state operators and wedge-locality in integrable quantum field theories

TL;DR

This paper investigates the construction of observable operators in two-dimensional integrable quantum field theories with poles in the S-matrix, focusing on the self-adjointness of bound state operators to ensure wedge-locality.

Contribution

It introduces a method to establish the strong commutativity of bound state operators by proving their essential self-adjointness, advancing the understanding of wedge-local observables.

Findings

Bound state operators constructed for theories with pole-containing S-matrices.

Essential self-adjointness shown for the two-particle component of the operators.

Conditions identified under which strong commutativity and wedge-locality are achieved.

Abstract

We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables in wedges. Under some additional assumptions on the S-matrix, we show that, in order to obtain their strong commutativity, it is enough to prove the essential self-adjointness of the sum of the left and right bound state operators. This essential self-adjointness is shown up to the two-particle component.