Annales Henri Poincaré

, Volume 6, Issue 2, pp 343–367 | Cite as

The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization

Original Paper

Abstract.

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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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.II. Mathematisches InstitutFreie Universität BerlinBerlinGermany
  2. 2.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  3. 3.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  4. 4.Department of Mathematics and Statistics, Center for Mathematical PhysicsBoston UniversityBostonUSA

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