2025 - T1 - Representation theory and noncommutative geometry

Collection 2025 - T1 - Representation theory and noncommutative geometry

Organizer(s) Afgoustidis, Alexandre ; Aubert, Anne-Marie ; Clare, Pierre ; Frahm, Jan ; Pasquale, Angela ; Şengün, Haluk

Date(s) 06/01/2025 - 04/04/2025

linked URL https://indico.math.cnrs.fr/event/10843/

110 112

Algebraic Quantum Field Theory and causal homogeneous spaces - Part 4a/4

By Karl-Hermann Neeb

Lorentzian manifolds and their conformal compactifications provide the most symmetric models of spacetimes. The structures studied on such spaces in Algebraic Quantum Field Theory (AQFT) are so-called nets of operator algebras, i.e., to each open subset ${\mathcal O}$ of the space-time manifold one associates a von Neumann algebra ${\mathcal M}({\mathcal O})$ in such a way that a certain natural list of axioms is satisfied.

We report on an ongoing project concerned with the construction of such nets on general causal homogeneous spaces $M = G/H$.

Lecture 4: Constructing nets of real subspaces.

Finally, we arrive at rather general characterizations of unitary representations and homogeneous spaces for which a rich supply of nets exists. Many classification results are still open and more bridges to Physics have to be built, but the overall structure of the theory takes shape.

Information about the video

Date of recording 21/03/2025
Date of publication 21/03/2025
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students, Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Darboux Amphitheater

Domain(s)

Operator Algebras

Bibliography

Lecture notes: https://en.www.math.fau.de/wp-content/uploads/sites/3/2025/03/qft-lect.pdf

MSC codes

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