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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Quantum Field Theory II

MP 8.6: Talk

Wednesday, March 20, 2024, 11:40–12:00, HL 001

Mourre theory and asymptotic observables in local relativistic quantum field theory — •Janik Kruse — Adam Mickiewicz University in Poznań, Uniwersytetu Poznańskiego 4, Poznań, Poland

A classical problem in scattering theory is the problem of asymptotic completeness (i.e. interpreting quantum theories in terms of particles). Asymptotic completeness is settled in non-relativistic quantum mechanics for many-body systems but a widely open problem in local relativistic quantum field theory (QFT). Many proofs of asymptotic completeness in quantum mechanics rely on the convergence of asymptotic observables. In QFT, Araki-Haag detectors have been identified as natural asymptotic observables. The convergence of Araki-Haag detectors on scattering states of bounded energy was established relatively early by Araki and Haag, but the convergence on arbitrary states has remained an open problem for decades. First convergence results of Araki-Haag detectors on arbitrary states have been obtained relatively recently by Dybalski and Gérard by translating quantum mechanical propagation estimates to QFT. They covered products of two or more Araki-Haag detectors sensitive to particles with distinct velocities, but the convergence of a single detector was not treated. The technical reason for this omission was a missing low velocity propagation estimate, which is usually proved by Mourre's conjugate operator method. So far, Mourre theory resisted any extension from quantum mechanics to quantum field theory. In a recent publication, we closed this gap and established the convergence of a single Araki-Haag detector. Based on https://arxiv.org/abs/2311.18680.

Keywords: Haag–Kastler quantum field theory; Haag–Ruelle scattering theory; Asymptotic completeness; Araki–Haag detectors; Mourre's conjugate operator method