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Renormalization of QED with planar binary trees

✍ Scribed by Ch. Brouder; A. Frabetti

Publisher
Springer-Verlag
Year
2001
Tongue
English
Weight
474 KB
Volume
19
Category
Article
ISSN
1434-6044

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πŸ“œ SIMILAR VOLUMES

QED Hopf algebras on planar binary trees
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✍ Christian Brouder; Alessandra Frabetti πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 190 KB

In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some semi-direct coproduct of Hopf algebras.

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Let k be a field and let S n be the symmetric group. The group algebra k[S n ] contains the Solomon descent algebra, which is of dimension 2 n&1 . In [MR] Malvenuto and Reutenauer construct a graded Hopf algebra structure on so that the sum of the Solomon descent algebras There is a basis In betw