Original Paper

Annales Henri Poincaré

, Volume 6, Issue 2, pp 343-367

First online:

The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization

  • Christoph BergbauerAffiliated withII. Mathematisches Institut, Freie Universität BerlinInstitut des Hautes Études Scientifiques Email author 
  • , Dirk KreimerAffiliated withInstitut des Hautes Études ScientifiquesDepartment of Mathematics and Statistics, Center for Mathematical Physics, Boston University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 +.