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arXiv · hep-th/0403207

The Hopf algebra of rooted trees in Epstein-Glaser renormalization

Christoph Bergbauer·Dirk Kreimer
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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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Christoph Bergbauer, Dirk Kreimer. 2005-02-10. The Hopf algebra of rooted trees in Epstein-Glaser renormalization. https://doi.org/10.1007/s00023-005-0210-3

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