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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Operator Algebras

MP 10.1: Hauptvortrag

Donnerstag, 3. April 2025, 14:00–14:30, ZHG001

Quantum field theory, quantum reference frames and the type of local algebras — •Christopher Fewster — Department of Mathematics, University of York, York, UK

This talk will be a more technically-oriented discussion of the material presented as a plenary talk with the same title during the conference.

QFT assigns local algebras of type III₁ to bounded open spacetime regions. However it has been argued that in some gravitational situations one must include an observer. This happens in particular for the static patch of de Sitter spacetime. Further, the physical observables should be joint observables of the combined QFT-observer system that are invariant under the joint time-evolution of the static patch and observer Hamiltonian. This algebra turns out to be of type II₁ [1]. In this talk, I will describe some of the details of a recent generalisation [2] which places the discussion of [1] on a more operational basis using QFT measurement schemes [3] and by reinterpreting the observer as a quantum reference frame.

[1] V. Chandrasekaran, R. Longo, G. Penington, and E. Witten, An algebra of observables for de Sitter space. JHEP 2023(2) 1-56.

[2] C.J. Fewster, D.W. Janssen, L.D. Loveridge, K. Rejzner and J. Waldron, Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory, Comm. Math. Phys., 406 (2025) 19:1-87

[3] C.J. Fewster and R. Verch, Quantum fields and local measurements, Comm. Math. Phys. 378 (2020) 851-889

Keywords: Algebraic quantum field theory; Quantum reference frames; von Neumann algebras