Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
Jins de Jong
TNO, Groningen, The NetherlandsAlexander Hock
University of Oxford, UKRaimar Wulkenhaar
University of Münster, Germany
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Abstract
Correlation functions in a dynamic quartic matrix model are obtained from the twopoint function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These “nested Catalan tables” have a description as diagrams of non-crossing chords and threads.
Cite this article
Jins de Jong, Alexander Hock, Raimar Wulkenhaar, Nested Catalan tables and a recurrence relation in noncommutative quantum field theory. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9 (2022), no. 1, pp. 47–72
DOI 10.4171/AIHPD/113