Combinatorial Hopf algebras from renormalization
Abstract
In this paper we describe the rightsided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the noncommutative version of the Faà di Bruno Hopf algebra, the noncommutative version of the charge renormalization Hopf algebra on planar binary trees for quantum electrodynamics, and the noncommutative version of the Pinter renormalization Hopf algebra on any bosonic field. We also describe two general ways to define the associative product in such Hopf algebras, the first one by recursion, and the second one by grafting and shuffling some decorated rooted trees.
 Publication:

arXiv eprints
 Pub Date:
 September 2009
 arXiv:
 arXiv:0909.3362
 Bibcode:
 2009arXiv0909.3362B
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics
 EPrint:
 16 pages