Combinatorial Hopf algebras from renormalization

@article{Brouder2009CombinatorialHA,
  title={Combinatorial Hopf algebras from renormalization},
  author={Christian Brouder and Alessandra Frabetti and Fr{\'e}d{\'e}ric Menous},
  journal={Journal of Algebraic Combinatorics},
  year={2009},
  volume={32},
  pages={557-578}
}
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 Faà 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… 

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