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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Quantenfeldtheorie I

MP 5.1: Hauptvortrag

Mittwoch, 2. März 2016, 16:45–17:30, VMP6 HS B

A criterion for asymptotic completeness in local relativistic QFT — •Wojciech Dybalski¹ and Christian Gerard² — ¹Technische Universität München — ²Universite Paris-Sud

It is well-known that the conventional property of asymptotic completeness fails in general in quantum field theory due to the possible presence of pairs of oppositely charged particles in the vacuum sector. In this talk we formulate a generalized concept of complete particle interpretation which takes this phenomenon into account: With the help of suitable asymptotic observables (Araki-Haag detectors) we construct a canonical `charged-pairs free' subspace. The generalized property of asymptotic completeness requires that this subspace coincides with the subspace of Haag-Ruelle scattering states. We show that this property holds in any massive quantum field theory satisfying the Haag-Kastler axioms. Our result can be reformulated as a criterion for conventional asymptotic completeness which should be sharp in theories with trivial superselection structure. The crucial technical step is the proof of convergence of the Araki-Haag detectors on all states from a suitable spectral subspace of the energy-momentum operators. This step is accomplished with the help of a novel propagation estimate, which is also relevant to scattering theory of quantum mechanical dispersive systems.