Direct construction of pointlike observables in the Ising model

TL;DR

This paper introduces a new method for explicitly constructing pointlike quantum fields in the Ising model, overcoming convergence issues and providing a concrete realization of local observables.

Contribution

It presents a novel approach to construct and verify pointlike fields directly as operators affiliated with local C*-algebras in the Ising model.

Findings

Explicit construction of all pointlike fields in the Ising model

Verification of the Reeh-Schlieder property for these fields

Demonstration that these fields generate local algebras

Abstract

The construction of pointlike fields in quantum integrable models is usually approached by constructing their n-point functions. However, convergence questions of the resulting infinite series remain unresolved even in the simplest case of the massive Ising model. On the other hand, the C*-algebraic approach to the construction considers semi-local bounded operators, but yields local operators only in a very abstract way. We use a novel approach to investigate the structure of these local observables, in the form of smeared pointlike quantum fields. Instead of considering their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with the local C*-algebras. We explicitly construct all pointlike fields of the Ising model, verify the Reeh-Schlieder property and show that they generate the local algebras by dualization.