Exploring the linear space of Feynman integrals via generating functions
arXiv:2306.02927
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.
11 pages, 4 figures, references added