Recursive structure of Baikov representations: Generics and application to symbology
Xuhang Jiang, Li Lin Yang
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 treelike 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. Nontrivial relations among these symbol letters can then be easily discovered using results from linear algebra.
Topics & Concepts
Symbol (formal)Feynman diagramFeynman integralAlgebra over a fieldMatrix (chemical analysis)Loop (graph theory)Computer sciencePure mathematicsMathematicsArithmeticCombinatoricsMathematical physicsProgramming languageMaterials scienceComposite materialAdvanced Topics in AlgebraAlgebraic structures and combinatorial modelsBlack Holes and Theoretical Physics