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Tropical Monte Carlo quadrature for Feynman integrals

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arxiv 2008.12310 v2 pith:OA4KVK7J submitted 2020-08-27 math-ph hep-thmath.AGmath.MP

Michael Borinsky This is my paper
classification math-phhep-thmath.AGmath.MP
keywords integralsfeynmanclassintegrandsmethodordertropicalalgebraic
verification ladder T0 review T1 audit T2 compute T3 formal
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We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The method can be improved further by exploiting the geometric structure of the underlying integrand. As an illustration of this, we give a specialized integration algorithm for a class of integrands that exhibit the form of a generalized permutahedron. This class includes integrands for scattering amplitudes and parametric Feynman integrals with tame kinematics. A proof-of-concept implementation is provided with which Feynman integrals up to loop order 17 can be evaluated.

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Cited by 7 Pith papers

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