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

Abstract

AbstractA 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+1which are interacting and asymptotically complete.