Araki-Haag approach to scattering in quantum field theories without mass gap

Haag-Ruelle scattering theory is a mathematical framework establishing an interpretation of quantum field theories in terms of scattering reactions of particles. Within the original Haag-Ruelle theory, relying on the mass-gap assumption, Huzihiro Araki and Rudolf Haag recognized the possibility to define a large family of asymptotic observables, which provide a mathematical modelling of experimental particle detectors. On the other hand, the Haag-Ruelle method for the construction of scattering states was adapted to the setting without mass gaps by Wojciech Dybalski building on previous work by Ira Herbst and Detlev Buchholz. In this framework, we extend the work of Araki and Haag to theories without mass gaps by proving the convergence of a family of Araki-Haag detectors on scattering states. Our proof relies on the decoupling assumption as introduced by Herbst, which is also required for the construction of scattering states. We further show, that the action of the asymptotic detectors on scattering states is completely described in terms of their action on the single-particle states, which provides additional evidence for the multi-particle interpretation of the scattering states.