Combinatorial Hopf algebras from renormalization. (English) Zbl 1211.81085
The right-sided combinatorial Hopf structure, as recently defined in the cofree-coassociative case by J.-L. Loday and M. Ronco [Combinatorial Hopf algebras. In: Clay Mathematical Proceedings (to appear)], of the three non-commutative Hopf algebras that describe the renormalization in quantum field theory is described by examining their linear duals. Two definitions of the associative product in these Hopf algebras are presented.
Reviewer: Eugene Kryachko (Liège)
MSC:
| 81T10 | Model quantum field theories |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 16T30 | Connections of Hopf algebras with combinatorics |
| 16T05 | Hopf algebras and their applications |
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
Keywords:
Hopf algebra; right-sided combinatorial Hopf structure; renormalization; quantum field theory; brace; treeReferences:
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