JournalsaihpdVol. 13, No. 1pp. 81–163

Combinatorial QFT on graphs: First quantization formalism

  • Ivan Contreras

    Amherst College, USA

  • Santosh Kandel

    California State University, Sacramento, USA

  • Pavel Mnev

    University of Notre Dame, USA; Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

  • Konstantin Wernli

    University of Southern Denmark, Odense M, Denmark
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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.

Cite this article

Ivan Contreras, Santosh Kandel, Pavel Mnev, Konstantin Wernli, Combinatorial QFT on graphs: First quantization formalism. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 13 (2026), no. 1, pp. 81–163

DOI 10.4171/AIHPD/194