A Criterion for Asymptotic Completeness in Local Relativistic QFT

Abstract

We formulate a generalized concept of asymptotic completeness and show that it holds in any Haag–Kastler quantum field theory with an upper and lower mass gap. It remains valid in the presence of pairs of oppositely charged particles in the vacuum sector, which invalidate the conventional property of asymptotic completeness. Our result can be restated as a criterion characterizing a class of theories with complete particle interpretation in the conventional sense. This criterion is formulated in terms of certain asymptotic observables (Araki–Haag detectors) whose existence, as strong limits of their approximating sequences, is our main technical result. It is proven with the help of a novel propagation estimate, which is also relevant to scattering theory of quantum mechanical dispersive systems.