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On Kreimer's Hopf algebra structure of Feynman graphs

  • T. Krajewski
  • R. Wulkenhaar
Theoretical physics

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

Field Theory Linear Combination Quantum Field Theory Hopf Algebra Algebra Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • T. Krajewski
    • 1
  • R. Wulkenhaar
    • 1
  1. 1. Centre de Physique Théorique, CNRS - Luminy, Case 907, 13288 Marseille Cedex 9, France FR

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