Vector Space of Feynman Integrals and Multivariate Intersection Numbers

Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for the construction of multivariate intersection numbers relevant to Feynman integrals, and show for the first time how they can be used to so...

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Bibliographic Details
Published in:Physical review letters Vol. 123; no. 20; p. 201602
Main Authors: Frellesvig, Hjalte, Gasparotto, Federico, Mandal, Manoj K., Mastrolia, Pierpaolo, Mattiazzi, Luca, Mizera, Sebastian
Format: Journal Article
Language:English
Published: United States American Physical Society 15.11.2019
Subjects:
Algorithms
Functional equations
Integrals
Multivariate analysis
Vector spaces
ISSN:0031-9007, 1079-7114, 1079-7114
Online Access:Get full text
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Summary:Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for the construction of 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 decomposition of a few Feynman integrals at one and two loops, as first steps toward potential applications to generic multiloop integrals. The proposed method can be more generally employed for the derivation of contiguity relations for special functions admitting multifold integral representations.
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ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.123.201602