The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization |
| |
| Authors: | Christoph Bergbauer Dirk Kreimer |
| |
| Affiliation: | (1) II. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin, Germany;(2) Institut des Hautes Études Scientifiques, F-91440 Bures-sur-Yvette, France;(3) Institut des Hautes Études Scientifiques, 35, route de Chartres, F-91440 Bures-sur-Yvette, France;(4) Department of Mathematics and Statistics, Center for Mathematical Physics, Boston University, Boston, MA 02215, USA |
| |
| 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+.submitted 29/03/04, accepted 01/06/04 |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
