Towards an explicit construction of local observables in integrable quantum field theories

TL;DR

This paper proposes a new approach to constructing local observables in integrable quantum field theories by establishing them as closed operators affiliated with local von Neumann algebras, focusing on scalar models like the massive Ising model.

Contribution

It introduces a novel framework for constructing local fields via wedge-local quantities and provides criteria for their existence, completing the construction for the massive Ising model.

Findings

Established criteria for the existence of averaged fields as closable operators.

Completed the construction of local observables in the massive Ising model.

Investigated the Reeh-Schlieder property and algebra generation by these fields.

Abstract

We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their $n$-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh-Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model.