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2019

Vector Space of Feynman Integrals and Multivariate Intersection Numbers

Frellesvig, Hjalte, Gasparotto, Federico, Mandal, Manoj K. et al.

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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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