2021 Impact factor 4.991
Particles and Fields
Eur. Phys. J. C 7, 697-708
DOI 10.1007/s100529801037

R. Wulkenhaar

On Kreimer's Hopf algebra structure of Feynman graphs

T. Krajewski - R. Wulkenhaar

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

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