Quantum fields on noncommutative geometries
Basic data for this talk
Type of talk: scientific talk
Name der Vortragenden: Wulkenhaar, Raimar
Date of talk: 08/12/2023
Talk language: English
Information about the event
Name of the event: Workshop on Operator Algebras and Applications: Non-Commutative Geometry
Event period: 04/12/2023 - 08/12/2023
Event location: Toronto
Organised by: Fields Institute
Abstract
Quantum field theories (QFT) in four dimensions tend to be trivial or difficult, often both. QFT on noncommutative geometries provide new examples to try. They are not admissible examples in the strict sense of axioms, but they share very similar challenges such as renormalisation and construction of products of distributions. Since there is a finite-dimensional approximation in terms of matrices, QFTs on noncommutative geometries come with a topological grading by the Euler characteristic of a Riemann surface. We give examples where the formal expansion in the Euler characteristic, together with topological recursion, permit to solve non-commutative QFT-models exactly. We also discuss how this topological expansion relates to questions in free probability.Keywords: quantum fields; noncommutative geometry; matrix models; topological recursion
Speakers from the University of Münster
| Wulkenhaar, Raimar | Professur für Reine Mathematik (Prof. Wulkenhaar) |