Hepp's bound for Feynman graphs and matroids
Mathematical Physics
2023-05-16 v3 High Energy Physics - Theory
Combinatorics
math.MP
Abstract
We study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to respect all known identities of Feynman integrals for graphs. We observe a strong correlation between the tropical and transcendental integrals, which yields a method to approximate unknown Feynman periods.
Cite
@article{arxiv.1908.09820,
title = {Hepp's bound for Feynman graphs and matroids},
author = {Erik Panzer},
journal= {arXiv preprint arXiv:1908.09820},
year = {2023}
}
Comments
78 pages, 26 figures, 1 ancillary file, v3 is identical to published version except for layout and cosmetic adjustments