Combinatorial QFT on graphs: first quantization formalism
Mathematical Physics
2023-08-16 v1 High Energy Physics - Theory
Combinatorics
math.MP
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
@article{arxiv.2308.07801,
title = {Combinatorial QFT on graphs: first quantization formalism},
author = {Ivan Contreras and Santosh Kandel and Pavel Mnev and Konstantin Wernli},
journal= {arXiv preprint arXiv:2308.07801},
year = {2023}
}
Comments
72 pages, 26 figures