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

Abstract

A recently developed $$n$$ 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 $$n$$ n -particle wave operators and the $$S$$ 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 $$S$$ 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 $$d > 1+1$$ d > 1 + 1 . Most notably, the Grosse–Lechner models provide the first examples of relativistic (wedge-local) QFT in space-time dimension $$d > 1+1$$ d > 1 + 1 which are interacting and asymptotically complete.