Geodesic
Hepp’s bound for Feynman graphs and matroids
Annales de l’Institut Henri Poincaré D, Tome 10 (2023) no. 1, pp. 31-119.

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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.

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DOI : 10.4171/aihpd/126
Classification : 81-XX, 05-XX, 52-XX
Keywords: Feynman integrals, tropicalization, Mellin transform, matroid invariants, panning tree polytope, matroid polytope, polytope volume 
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     title = {Hepp{\textquoteright}s bound for {Feynman} graphs and matroids},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/126/}
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Panzer, Erik. Hepp’s bound for Feynman graphs and matroids. Annales de l’Institut Henri Poincaré D, Tome 10 (2023) no. 1, pp. 31-119. doi : 10.4171/aihpd/126. http://geodesic.mathdoc.fr/articles/10.4171/aihpd/126/

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