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D-module techniques for solving differential equations in the context of Feynman integrals
Max Planck Inst Phys & Astrophys, Boltzmannstr 8, D-85748 Garching, Germany..
Univ Calif Berkeley, Dept Math, 970 Evans Hall 3840, Berkeley, CA 94720 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany.ORCID iD: 0000-0002-2308-4070
Univ Torino, Dipartimento Fis, Turin, Italy.;Univ Torino, Arnold Regge Ctr, Turin, Italy.;INFN, Sez Torino, Via P Giuria 1, I-10125 Turin, Italy.;CERN, Theoret Phys Dept, CH-1211 Geneva 23, Switzerland..
2024 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 114, no 3, article id 87Article in journal (Refereed) Published
Abstract [en]

Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compare D-module methods to dedicated methods developed for solving differential equations appearing in the context of Feynman integrals, and provide a dictionary of the relevant concepts. In particular, we implement an algorithm due to Saito, Sturmfels, and Takayama to derive canonical series solutions of regular holonomic D-ideals, and compare them to asymptotic series derived by the respective Fuchsian systems.

Place, publisher, year, edition, pages
Springer Nature , 2024. Vol. 114, no 3, article id 87
Keywords [en]
Feynman integrals, D-modules, Differential equations, Conformal symmetry
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-350156DOI: 10.1007/s11005-024-01835-7ISI: 001252373800001Scopus ID: 2-s2.0-85196507834OAI: oai:DiVA.org:kth-350156DiVA, id: diva2:1885394
Note

QC 20240723

Available from: 2024-07-23 Created: 2024-07-23 Last updated: 2024-07-23Bibliographically approved

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Sattelberger, Anna-Laura

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