A criterion for asymptotic completeness in local relativistic QFT

TL;DR

This paper introduces a generalized criterion for asymptotic completeness in local relativistic quantum field theories, accommodating cases with oppositely charged particles, and provides new technical tools for scattering analysis.

Contribution

It formulates a new criterion for asymptotic completeness applicable to a broader class of quantum field theories, including those with charged particle pairs.

Findings

Asymptotic completeness holds in Haag-Kastler QFT with mass gaps.

The criterion remains valid with oppositely charged particle pairs.

A novel propagation estimate aids scattering theory analysis.

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.