Combinatorial QFT on graphs: First quantization formalism

Ivan Contreras, Santosh Kandel, Pavel Mnev, Konstantin Wernli

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We study a combinatorial model of the quantum scalar field with polynomial potential on a graph. In the first quantization formalism, the value of a Feynman graph is given by a sum over maps from the Feynman graph to the spacetime graph (mapping edges to paths). This picture interacts naturally with Atiyah–Segal-like cutting-gluing of spacetime graphs. In particular, one has combinatorial counterparts of the known gluing formulae for Green’s functions and (zeta-regularized) determinants of Laplacians.
Original languageEnglish
JournalAnnales de l’Institut Henri Poincaré D
ISSN2308-5827
DOIs
Publication statusE-pub ahead of print - 3. Jun 2024

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