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arXiv · 2306.02927

Exploring the linear space of Feynman integrals via generating functions

Xin Guan·Xiang Li·Yan-Qing Ma
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Abstract

Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and solving differential equations of these generating functions, we are able to derive a system of reduction rules that effectively reduce any associated Feynman integrals to their bases. We illustrate this method through various examples and observe its potential value in numerous scenarios.

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Xin Guan, Xiang Li, Yan-Qing Ma. 2023-06-05. Exploring the linear space of Feynman integrals via generating functions. https://arxiv.org/abs/2306.02927

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