Quantum fields on noncommutative geometries

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Abstract

Quantum field theories (QFT) in four dimensions tend to be trivial or difficult, and often both. QFT on noncommutative geometries provide new examples to explore. They are not admissible examples in the strict sense of axioms, but they share very similar challenges such as renormalisation and a construction of products of distributions. Whenever there is a finite-dimensional approximation of quantum spaces in terms of matrices, QFT 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 us to obtain exact solutions for noncommutative QFT-models. To end with, we will also discuss how the above topological expansion relates to questions in free probability.

Speakers from the University of Münster

Wulkenhaar, Raimar

Professur für Reine Mathematik (Prof. Wulkenhaar)