Asymptotic completeness in a class of massless relativistic quantum field theories

TL;DR

This paper introduces the first examples of interacting, asymptotically complete massless relativistic quantum field theories in two dimensions, constructed via a deformation of chiral conformal theories, with preserved scattering properties.

Contribution

It demonstrates the construction of interacting, asymptotically complete massless QFTs using a deformation method applied to chiral conformal theories, expanding the class of known models.

Findings

Models are not strictly local but contain wedge-localized observables.

Scattering theory remains valid under weaker localization assumptions.

First examples of such theories with these properties are provided.

Abstract

This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.