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arXiv · 2303.11105

$D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals

Johannes Henn·Elizabeth Pratt·Anna-Laura Sattelberger·Simone Zoia
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Abstract

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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Johannes Henn, Elizabeth Pratt, Anna-Laura Sattelberger, Simone Zoia. 2023-03-20. $D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals. https://doi.org/10.1007/s11005-024-01835-7

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