TL;DR
This review paper summarizes the properties of Feynman graph polynomials, which are key to understanding multi-loop integrals in quantum field theory, covering topics like spanning trees, minors, and matroids.
Contribution
It provides a comprehensive overview of mathematical properties and identities related to Feynman graph polynomials, integrating concepts from graph theory and matroid theory.
Findings
Detailed properties of Feynman graph polynomials
Connections to spanning trees and forests
Recursion relations and identities like Dodgson's
Abstract
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
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