Quantum fields on noncommutative geometries

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Zusammenfassung

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.

Vortragende der Universität Münster

Wulkenhaar, Raimar

Professur für Reine Mathematik (Prof. Wulkenhaar)