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Copositive geometry of Feynman integrals

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arxiv 2504.01628 v2 pith:WROZQXEK submitted 2025-04-02 math.OC hep-thmath-phmath.COmath.MP

Bernd Sturmfels , Máté L. Telek This is my paper · ORCID
classification math.OChep-thmath-phmath.COmath.MP
keywords copositivefeynmanconegeometryintegralsalgebraicboundaryconnect
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Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone. P\'olya's method makes this manifest. We study the copositive cone for the second Symanzik polynomial of any Feynman graph. Its algebraic boundary is described by Landau discriminants.

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  1. Global Convergence of the Return Dynamics in the Class $\mathcal{O}_C$

    math.DS 2026-03 unverdicted novelty 6.0 of 10

    Return dynamics on class O_C domains with fixed convex core converge globally like adaptive gradient descent of the thickness function, with fixed points equal to thickness critical points.

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