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Wulkenhaar, Raimar

Quantum field theory on noncommutative spaces. (English) Zbl 1482.81038

Chamseddine, Ali (ed.) et al., Advances in noncommutative geometry. Based on the noncommutative geometry conference, Shanghai, China, March 23 – April 7, 2017. On the occasion of Alain Connes’ 70th Birthday. Cham: Springer. 607-690 (2019).
Summary: This survey tries to give a rigorous definition of Euclidean quantum field theory on a fairly large class of noncommutative geometries, namely nuclear AF Fréchet algebras. After a review of historical developments and current trends we describe in detail the construction of the \(\Phi^3\)-model and explain its relation to the Kontsevich model. We review the current status of the construction of the \(\Phi^4\)-model and present in an outlook a possible definition of Schwinger functions for which the Osterwalder-Schrader axioms can be formulated.
For the entire collection see [Zbl 1432.58003].

Cited in 4 Documents

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81T08 Constructive quantum field theory
81T10 Model quantum field theories
81T05 Axiomatic quantum field theory; operator algebras
81R60 Noncommutative geometry in quantum theory
46A04 Locally convex Fréchet spaces and (DF)-spaces

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