The recursive structure of Baikov representations I: generics and application to symbology

Abstract

In this paper, we explore the recursive structure of Baikov representations for Feynman integrals. We demonstrate that the various Baikov representations for all sectors of an integral family can be organized in a tree-like structure. Using this structure, we show that the symbol letters of one-loop Feynman integrals can be written in terms of minors of a matrix associated with the top sector. Non-trivial relations among these symbol letters can then be easily discovered using results from linear algebra.

arXiv commentmatched with published version, package BaikovAll.wl added in supplemental material

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• SOFIA: Singularities of Feynman Integrals Automatized
• Intersection Numbers from Companion Tensor Algebra
• The recursive structure of Baikov representations II: the top-down reduction with intersection theory
• General Relativity from Intersection Theory