Asymptotic Completeness in a Class of Massive Wedge-Local Quantum Field Theories in any Dimension

TL;DR

This paper demonstrates that certain wedge-local quantum field theories in higher dimensions are asymptotically complete and interacting, providing explicit formulas for scattering operators and showing stability under deformation, thus advancing understanding of relativistic QFT.

Contribution

It establishes asymptotic completeness for a class of wedge-local QFT models in any dimension, with explicit scattering formulas and stability under BLS-deformation, including novel higher-dimensional examples.

Findings

Explicit expressions for n-particle wave operators and S-matrix.

Ordered asymptotic completeness is stable under BLS-deformation.

Grosse-Lechner models are the first higher-dimensional interacting, asymptotically complete wedge-local QFTs.

Abstract

A recently developed n-particle scattering theory for wedge-local quantum field theories is applied to a class of models described and constructed by Grosse, Lechner, Buchholz, and Summers. In the BLS-deformation setting we establish explicit expressions for n-particle wave operators and the S-matrix of ordered asymptotic states, and we show that ordered asymptotic completeness is stable under the general BLS-deformation construction. In particular the (ordered) Grosse-Lechner S-matrices are non-trivial also beyond two-particle scattering and factorize into 2-particle scattering processes, which is an unusual feature in space-time dimension d > 1 + 1. Most notably, the Grosse-Lechner models provide the first examples of relativistic (wedge-local) QFT in space-time dimension d > 1 + 1 which are interacting and asymptotically complete.