D-module techniques for solving differential equations in the context of Feynman integrals

被引:1
作者
Henn, Johannes [1 ]
Pratt, Elizabeth [2 ]
Sattelberger, Anna-Laura [3 ,4 ]
Zoia, Simone [5 ,6 ,7 ,8 ]
机构
[1] Max Planck Inst Phys & Astrophys, Boltzmannstr 8, D-85748 Garching, Germany
[2] Univ Calif Berkeley, Dept Math, 970 Evans Hall 3840, Berkeley, CA 94720 USA
[3] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
[4] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
[5] Univ Torino, Dipartimento Fis, Turin, Italy
[6] Univ Torino, Arnold Regge Ctr, Turin, Italy
[7] INFN, Sez Torino, Via P Giuria 1, I-10125 Turin, Italy
[8] CERN, Theoret Phys Dept, CH-1211 Geneva 23, Switzerland
关键词
Feynman integrals; D-modules; Differential equations; Conformal symmetry; CONFORMAL SYMMETRY; ALGORITHM; DIAGRAMS; SYSTEMS;
D O I
10.1007/s11005-024-01835-7
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
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页数:51
相关论文
共 67 条
[1]  
Agostini D, 2024, Arxiv, DOI arXiv:2208.08967
[2]   FeynGKZ: A Mathematica package for solving Feynman integrals using GKZ hypergeometric systems [J].
Ananthanarayan, B. ;
Banik, Sumit ;
Bera, Souvik ;
Datta, Sudeepan .
COMPUTER PHYSICS COMMUNICATIONS, 2023, 287
[3]   Scalar one-loop integrals using the negative-dimension approach [J].
Anastasiou, C ;
Glover, EWN ;
Oleari, C .
NUCLEAR PHYSICS B, 2000, 572 (1-2) :307-360
[4]   Constructive D-Module Theory with SINGULAR [J].
Andres, Daniel ;
Brickenstein, Michael ;
Levandovskyy, Viktor ;
Martin-Morales, Jorge ;
Schoenemann, Hans .
MATHEMATICS IN COMPUTER SCIENCE, 2010, 4 (2-3) :359-383
[5]  
[Anonymous], 1965, Pure and Applied Mathematics
[6]   Feynman diagrams and differential equations [J].
Argeri, Mario ;
Mastrolia, Pierpaolo .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2007, 22 (24) :4375-4436
[7]   Real-time finite-temperature correlators from AdS/CFT [J].
Barnes, Edwin ;
Vaman, Diana ;
Wu, Chaolun ;
Arnold, Peter .
PHYSICAL REVIEW D, 2010, 82 (02)
[8]   Lorentzian CFT 3-point functions in momentum space [J].
Bautista, Teresa ;
Godazgar, Hadi .
JOURNAL OF HIGH ENERGY PHYSICS, 2020, 2020 (01)
[9]   Feynman integral relations from parametric annihilators [J].
Bitoun, Thomas ;
Bogner, Christian ;
Klausen, Rene Pascal ;
Panzer, Erik .
LETTERS IN MATHEMATICAL PHYSICS, 2019, 109 (03) :497-564
[10]  
Boege T., 2023, Eur. Math. Soc. Mag., V130, P40, DOI [10.4171/mag/152, DOI 10.4171/MAG/152]