Annales Henri Poincaré

, Volume 6, Issue 2, pp 343–367

The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization


    • II. Mathematisches InstitutFreie Universität Berlin
    • Institut des Hautes Études Scientifiques
  • Dirk Kreimer
    • Institut des Hautes Études Scientifiques
    • Department of Mathematics and Statistics, Center for Mathematical PhysicsBoston University
Original Paper

DOI: 10.1007/s00023-005-0210-3

Cite this article as:
Bergbauer, C. & Kreimer, D. Ann. Henri Poincaré (2005) 6: 343. doi:10.1007/s00023-005-0210-3


We show how the Hopf algebra of rooted trees encodes the combinatorics of Epstein-Glaser renormalization and coordinate space renormalization in general. In particular, we prove that the Epstein-Glaser time-ordered products can be obtained from the Hopf algebra by suitable Feynman rules, mapping trees to operator-valued distributions. Twisting the antipode with a renormalization map formally solves the Epstein-Glaser recursion and provides local counterterms due to the Hochschild 1-closedness of the grafting operator B+.

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© Birkhäuser Verlag, Basel 2005