$D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910967776935936 |
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| author | Henn, Johannes Pratt, Elizabeth Sattelberger, Anna-Laura Zoia, Simone |
| author_facet | Henn, Johannes Pratt, Elizabeth Sattelberger, Anna-Laura Zoia, Simone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11105 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals Henn, Johannes Pratt, Elizabeth Sattelberger, Anna-Laura Zoia, Simone High Energy Physics - Theory Symbolic Computation Algebraic Geometry Classical Analysis and ODEs 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. |
| title | $D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals |
| topic | High Energy Physics - Theory Symbolic Computation Algebraic Geometry Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2303.11105 |