Hepp's bound for Feynman graphs and matroids

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.

78 pages, 26 figures, 1 ancillary file, v3 is identical to published version except for layout and cosmetic adjustments

References in corpus (8)

• Resolution of singularities for multi-loop integrals
• Hepp's bound for Feynman graphs and matroids
• Strict log-concavity of the Kirchhoff polynomial and its applications to the strong Lefschetz property
• Toric geometry and regularization of Feynman integrals
• Relativistic causality and position space renormalization
• A special case of completion invariance for the $c_2$ invariant of a graph
• Tensor structure from scalar Feynman matroids
• Another approach to volume of matroid polytopes

Cited by in corpus (16)

• Tropical Feynman integration in the Minkowski regime
• Hepp's bound for Feynman graphs and matroids
• Unitarity Cuts of the Worldsheet
• Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra
• Four Lectures on Euler Integrals
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• Graph complexes and Feynman rules
• The Asymptotic Structure of Cosmological Integrals
• Statistics of Feynman amplitudes in ${\varphi }^4$-theory
• Momentum Space Landau Equations Via Isotopy Techniques
• Algebraic Interplay between Renormalization and Monodromy
• Predicting Feynman periods in ${\varphi }^4$-theory
• Tropical sampling from Feynman measures
• Feynman integrals at large loop order and the $\log$-$\Gamma$ distribution
• Tropicalized quantum field theory and global tropical sampling
• Tropical Feynman integration in the physical region