On the status of pointlike fields in integrable QFTs

TL;DR

This paper proposes a hybrid method to construct pointlike local quantum fields in integrable quantum field theories, establishing their existence as closed operators affiliated with local von Neumann algebras, demonstrated in the Ising model.

Contribution

It introduces a new hybrid approach to construct pointlike fields in integrable QFTs, bridging wedge-local methods and explicit pointlike field construction.

Findings

Successful construction of pointlike fields in the Ising model

Establishment of fields as closed operators affiliated with local algebras

Provides a new perspective on local field existence in integrable QFTs

Abstract

In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their $n$-point functions is unclear in this setting. An alternative approach uses fully convergent expressions for fields with weaker localization properties in spacelike wedges, and deduces existence of observables in bounded regions from there, but yields little information about their explicit form. We propose a new, hybrid construction: We aim to describe pointlike local quantum fields; but rather than exhibiting their $n$-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with a net of local von Neumann algebras that is known from the wedge-local approach. This is shown to work at least in the Ising model.