English

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.

Keywords

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

R2 v1 2026-06-23T10:57:11.418Z