On Kreimer's Hopf algebra structure of Feynman graphs
Abstract
We reinvestigate Kreimer's Hopf algebra structure of perturbative quantum field theories with a special emphasis on overlapping divergences. Kreimer first disentangles overlapping divergences into a linear combination of disjoint and nested ones and then tackles that linear combination by the Hopf algebra operations. We present a formulation where the Hopf algebra operations are directly defined on any type of divergence. We explain the precise relation to Kreimer's Hopf algebra and obtain thereby a characterization of their primitive elements.
Keywords
Cite
@article{arxiv.hep-th/9805098,
title = {On Kreimer's Hopf algebra structure of Feynman graphs},
author = {Thomas Krajewski and Raimar Wulkenhaar},
journal= {arXiv preprint arXiv:hep-th/9805098},
year = {2011}
}
Comments
21 pages, LaTeX2e, requires feynmf package to draw Feynman graphs (see log file for additional information). Following an idea by Dirk Kreimer we introduced in the revised version a primitivator which maps overlapping divergences to primitive elements and which provides the link to the Hopf algebra of Kreimer (q-alg/9707029, hep-th/9808042). v4: error in eq (29) corrected and references updated; to appear in Eur.Phys.J. C