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arXiv · hep-th/9805098

On Kreimer's Hopf algebra structure of Feynman graphs

Thomas Krajewski·Raimar Wulkenhaar
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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.

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Thomas Krajewski, Raimar Wulkenhaar. 1998-11-04. On Kreimer's Hopf algebra structure of Feynman graphs. https://doi.org/10.1007/s100529801037

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