# 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…

## 13 Citations

### Combinatorial Hopf algebras

- Mathematics
- 2008

We define a "combinatorial Hopf algebra" as a Hopf algebra which is free (or cofree) and equipped with a given isomorphism to the free algebra over the indecomposables (resp. the cofree coalgebra…

### Non-perturbative graph languages, halting problem and complexity

- Computer ScienceForum Mathematicum
- 2022

Abstract We explain the foundations of a new class of formal languages for the construction of large Feynman diagrams which contribute to solutions of all combinatorial Dyson–Schwinger equations in a…

### Loop of formal diffeomorphisms and Faà di Bruno coloop bialgebra

- MathematicsAdvances in Mathematics
- 2019

### Weighted infinitesimal unitary bialgebras of rooted forests, symmetric cocycles and pre-Lie algebras

- Mathematics
- 2020

The concept of weighted infinitesimal unitary bialgebra is an algebraic meaning of the nonhomogenous associative Yang–Baxter equation. In this paper, we equip the space of decorated planar rooted…

### Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

- Physics
- 2014

We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions…

### Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization

- Mathematics
- 2010

The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the…

### A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory

- Physics
- 2018

This monograph aims to build some new mathematical structures originated from Dyson--Schwinger equations for the description of non-perturbative aspects of gauge field theories whenever bare or…

### Graphons and renormalization of large Feynman diagrams

- Physics
- 2018

The article builds a new enrichment of the Connes-Kreimer renormalization Hopf algebra of Feynman diagrams in the language of graph functions.

### Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles

- MathematicsPacific Journal of Mathematics
- 2019

In this paper, we define a new coproduct on the space of decorated planar rooted forests to equip it with a weighted infinitesimal unitary bialgebraic structure. We introduce the concept of…

### Weighted infinitesimal bialgebras

- Mathematics
- 2018

As a uniform of two versions of infinitesimal bialgebras introduced respectively by Joni-Rota and Loday-Ronco, weighted infinitesimal bialgebras play an important role in mathematics and mathematical…

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