Copositive geometry of Feynman integrals
Optimization and Control
2025-06-24 v2 High Energy Physics - Theory
Mathematical Physics
Combinatorics
math.MP
Abstract
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.
Cite
@article{arxiv.2504.01628,
title = {Copositive geometry of Feynman integrals},
author = {Bernd Sturmfels and Máté L. Telek},
journal= {arXiv preprint arXiv:2504.01628},
year = {2025}
}
Comments
Final version to appear in Letters in Mathematical Physics