DOI 10.1007/s100529801037
R. Wulkenhaar
On Kreimer's Hopf algebra structure of Feynman graphs
Centre de Physique Théorique, CNRS - Luminy, Case 907, 13288 Marseille Cedex 9, France
Received: 9 July 1998 / Revised version: 21 September 1998 / Published online: 19 November 1998
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.
Copyright Springer-Verlag
