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arXiv · 1907.02000

Vector Space of Feynman Integrals and Multivariate Intersection Numbers

Hjalte Frellesvig·Federico Gasparotto·Manoj K. Mandal·Pierpaolo Mastrolia·Luca Mattiazzi·Sebastian Mizera
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Abstract

Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals, and show for the first time how they can be used to solve the problem of integral reduction to a basis of master integrals by projections, and to directly derive functional equations fulfilled by the latter. We apply it to the derivation of contiguity relations for special functions admitting multi-fold integral representations, and to the decomposition of a few Feynman integrals at one- and two-loops, as first steps towards potential applications to generic multi-loop integrals.

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Hjalte Frellesvig, Federico Gasparotto, Manoj K. Mandal, Pierpaolo Mastrolia, Luca Mattiazzi, Sebastian Mizera. 2019-07-03. Vector Space of Feynman Integrals and Multivariate Intersection Numbers. https://doi.org/10.1103/physrevlett.123.201602

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