Combinatorial QFT on graphs: First quantization formalism

doi:10.4171/AIHPD/194

Combinatorial QFT on graphs: First quantization formalism

2026-01-01

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DOI：10.4171/AIHPD/194

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Abstract

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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.

Keywords:

functorial QFT

combinatorial QFT

first quantization formalism

scalar field with polynomial potential

perturbative path integral

Feynman diagrams

Combinatorial QFT on graphs: First quantization formalism

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