A Characterization Theorem for Local Operators in Factorizing Scattering Models

TL;DR

This paper provides an explicit characterization of local observables in integrable quantum field theories, advancing the understanding of their structure and domain properties, with applications demonstrated in the quantum Ising model.

Contribution

It introduces a new characterization of local operators based on coefficient functions, extending previous abstract existence proofs to explicit constructions.

Findings

Explicit local observables constructed in the quantum Ising model

Characterization of operator domains for local observables

Enhanced understanding of local operators in integrable QFTs

Abstract

In quantum field theory, the rigorous construction of local observables in the presence of nontrivial interaction is a crucial problem. In a class of integrable quantum field theories, a very abstract existence proof has recently been given by Lechner. We give an explicit characterization of these local observables in terms of the properties of the coefficient functions in an expansion by interacting creators and annihilators. Some results on the operator domains of these local observables are given. Using these, we constructed explicit examples of local observables in the quantum Ising model.