2014/07/19 by Kreimer, Dirk
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1407.5150
We discuss structural similarities between Knizhnik--Zamolodchikov equations (in fact, their simplest version needed to introduce the Drinfeld associator) and Dyson--Schwinger equations. We emphasize that the latter allow for a filtration by co-radical degree using quasi-shuffle products and the lower central series filtration of the Lie algebra of Feynman graphs. This clarifies how they are a generalization of the KZ equations. This is a starting point for a algebraic organization of the next-to...-to leading log expansion which has been worked out in collaboration with Olaf Krueger and which will be given elsewhere [1,2].