Quantum field theory on noncommutative spaces

Raimar Wulkenhaar ()
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Raimar Wulkenhaar: Mathematisches Institut der Westfälischen Wilhelms-Universität

A chapter in Advances in Noncommutative Geometry, 2019, pp 607-690 from Springer

Abstract: Abstract 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 Φ3-model and explain its relation to the Kontsevich model. We review the current status of the construction of the Φ4-model and present in an outlook a possible definition of Schwinger functions for which the Osterwalder–Schrader axioms can be formulated.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-29597-4_11

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DOI: 10.1007/978-3-030-29597-4_11

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