The Hopf algebra of rooted trees in Epstein-Glaser renormalization

Details The Hopf algebra of rooted trees in Epstein-Glaser renormalization The Hopf algebra of rooted trees in Epstein-Glaser renormalization

2004-03-22

arxiv.org/abs/hep-th/0403207v2

Annales Henri Poincare 6 (2005) 343-367

Physics

High Energy Physics

High Energy Physics - Theory

19p, minor corrections and improvements. To appear in AHP

Scientific paper

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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