# Mourre theory and asymptotic observables in local relativistic quantum field theory

November 30, 2023

We prove the convergence of Araki-Haag detectors in Haag-Kastler quantum field theory with an upper and lower mass gap. We cover the case of a single Araki-Haag detector on states of bounded energy, which are selected from the absolutely continuous part of the energy-momentum spectrum below the three-particle threshold. In our proof, we apply Mourre's conjugate operator method for the first time in Haag-Kastler quantum field theory. Taking quantum mechanical proofs of asymptotic completeness as a guide, these advances bring us closer to understanding two-particle asymptotic completeness in local relativistic quantum field theory.

Keywords:

Haag-Kastler quantum field theory, Haag-Ruelle scattering theory, asymptotic completeness, asymptotic observables, Araki-Haag detectors, Mourreās conjugate operator method