Combinatorial Hopf algebras from renormalization

Details Combinatorial Hopf algebras from renormalization Combinatorial Hopf algebras from renormalization

2009-09-18

arxiv.org/abs/0909.3362v2

Journal of Algebraic Combinatorics (2010) online

Mathematics

Quantum Algebra

16 pages

Scientific paper

10.1007/s10801-010-0227-7

In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the non-commutative version of the charge renormalization Hopf algebra on planar binary trees for quantum electrodynamics, and the non-commutative 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.

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