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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Field Theory I: Axiomatic, Probabilistic, Algebraic, Conformal

MP 3.4: Vortrag

Dienstag, 17. März 2026, 17:45–18:00, KH 02.013

Applications of the Lax-Phillips Theorem in Algebraic Quantum Field Theory — •Jonas Schober — Brigham Young University, Provo, Utah, USA

Algebraic quantum field theory is one of the main attempts to provide a formal mathematical framework for quantum field theory. Its core idea is to assign to every space-time region a von Neumann algebra of local observables, subject to the Haag-Kastler axioms, which encode locality, covariance, and causality. Translating the Haag-Kastler axioms from von Neumann algebras to the simpler setting of so-called standard subspaces leads to the investigation of one-parameter semigroups of unitary endomorphisms of standard subspaces. In this talk, we show how a real version of the classical Lax-Phillips Theorem, originally developed in the context of scattering theory, can be used to represent these endomorphism semigroups in an L²-space over the real line. We also outline how this concrete realization allows one to obtain structural results about the semigroups.

Keywords: AQFT; Haag-Kastler; Von Neumann Algebras; Standard Subspaces; Lax-Phillips