Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 6

Graph minors and the linear reducibility of Feynman diagrams

Pages: 1657 – 1683

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n6.a6

Authors

Benjamin Moore (Dept. of Combinatorics and Optimization, University of Waterloo, Ontario, Canada)

Karen Yeats (Dept. of Combinatorics and Optimization, University of Waterloo, Ontario, Canada)

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.

Full Text (PDF format)

The authors would like to thank NSERC for financial support. This work was partially completed while both authors were at Simon Fraser University.

Published 20 March 2020