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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| Published in: | Physical review letters Vol. 123; no. 20; p. 201602 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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American Physical Society
15.11.2019
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| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
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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 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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| AbstractList | 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.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. 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. |
| ArticleNumber | 201602 |
| Author | Mandal, Manoj K. Mastrolia, Pierpaolo Gasparotto, Federico Frellesvig, Hjalte Mattiazzi, Luca Mizera, Sebastian |
| Author_xml | – sequence: 1 givenname: Hjalte surname: Frellesvig fullname: Frellesvig, Hjalte – sequence: 2 givenname: Federico surname: Gasparotto fullname: Gasparotto, Federico – sequence: 3 givenname: Manoj K. surname: Mandal fullname: Mandal, Manoj K. – sequence: 4 givenname: Pierpaolo orcidid: 0000-0001-9711-7798 surname: Mastrolia fullname: Mastrolia, Pierpaolo – sequence: 5 givenname: Luca surname: Mattiazzi fullname: Mattiazzi, Luca – sequence: 6 givenname: Sebastian surname: Mizera fullname: Mizera, Sebastian |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/31809080$$D View this record in MEDLINE/PubMed |
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