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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Communicated by Vincent Rivasseau
submitted 29/03/04, accepted 01/06/04
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Bergbauer, C., Kreimer, D. The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization. Ann. Henri Poincaré 6, 343–367 (2005). https://doi.org/10.1007/s00023-005-0210-3
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DOI: https://doi.org/10.1007/s00023-005-0210-3