Graph Minors and the Linear Reducibility of Feynman Diagrams

TL;DR

This paper investigates the structural properties of Feynman diagrams related to graph minors and their reducibility, providing insights into the classification of diagrams based on their polynomial reducibility and known forbidden minors.

Contribution

It establishes that reducibility with respect to Symanzik polynomials is graph minor closed for diagrams with fixed external momenta, and surveys known structural results and forbidden minors.

Findings

Reducibility is graph minor closed for fixed external momenta.

Survey of known forbidden minors and structural results.

Provides structural insights into reducible Feynman diagrams.

Abstract

We look at a graph property called reducibility which is closely related to a condition developed by Brown to evaluate Feynman integrals. We show for graphs with a fixed number of external momenta, that reducibility with respect to both Symanzik polynomials is graph minor closed. We also survey the known forbidden minors and the known structural results. This gives some structural information on those Feynman diagrams which are reducible.