Modular Nuclearity and Localization

TL;DR

This paper introduces a spectral nuclearity condition in algebraic quantum field theory that ensures the existence of localized observables within wedge regions in two-dimensional Minkowski space, advancing the algebraic approach to the formfactor program.

Contribution

It proposes a new nuclearity-based condition for the non-trivial intersection of wedge algebras, providing a method to identify local observables in algebraic QFT.

Findings

The condition guarantees non-trivial intersections of wedge algebras.

Illustrated with simple examples demonstrating the condition's application.

Advances the algebraic approach to the formfactor program.

Abstract

Within the algebraic setting of quantum field theory, a condition is given which implies that the intersection of algebras generated by field operators localized in wedge--shaped regions of two--dimensional Minkowski space is non--trivial; in particular, there exist compactly localized operators in such theories which can be interpreted as local observables. The condition is based on spectral (nuclearity) properties of the modular operators affiliated with wedge algebras and the vacuum state and is of interest in the algebraic approach to the formfactor program, initiated by Schroer. It is illustrated here in a simple class of examples.