On Kreimer's Hopf algebra structure of Feynman graphs

We reinvestigate Kreimer's Hopf algebra structure of perturbative quantum f ield theories with a special emphasis on overlapping divergences. Kreimer f irst disentangles overlapping divergences into a linear combination of disj oint and nested ones and then tackles that linear combination by the Hopf a lgebra operations. We present a formulation where the Hopf algebra operatio ns are directly defined on any type of divergence. We explain the precise r elation to Kreimer's Hopf algebra and obtain thereby a characterization of their primitive elements.