Berlin 2014 – wissenschaftliches Programm
MP 10.1: Vortrag
Donnerstag, 20. März 2014, 14:40–15:00, SPA SR125
Araki-Haag Approach to Scattering in Quantum Field Theories without Mass Gap — •Maximilian Duell1 and Wojciech Dybalski1,2 — 1Zentrum Mathematik, Technische Universität München, D-85747 Garching, Germany — 2Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich, 8093 Zürich, Switzerland
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.