费曼积分背景下求解微分方程的 D 模块技术

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-06-21 DOI:10.1007/s11005-024-01835-7

Johannes Henn, Elizabeth Pratt, Anna-Laura Sattelberger, Simone Zoia

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引用次数: 0

摘要

费曼积分是具有多项式系数的线性偏微分方程的解。以具有一般指数的三角积分为例，我们将 D 模块方法与为求解费曼积分背景下出现的微分方程而开发的专用方法进行了比较，并提供了相关概念的词典。特别是，我们实现了由 Saito、Sturmfels 和 Takayama 提出的算法，推导出规则整体 D-ideals的典范级数解，并将其与由相应的 Fuchsian 系统推导出的渐近级数进行比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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

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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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.