# TOPICAL REVIEW: The Hopf algebra approach to Feynman diagram calculations

@article{EbrahimiFard2005TOPICALRT, title={TOPICAL REVIEW: The Hopf algebra approach to Feynman diagram calculations}, author={Kurusch Ebrahimi-Fard and Dirk Kreimer}, journal={Journal of Physics A}, year={2005} }

Two directional measuring device having an elongate measuring member having a distance measuring scale along its length and another measuring member to measure distance in another direction. The two members are relatively moveable in the direction of the measuring scale of the elongate member and the other member has diverging surfaces extending generally in that direction and a distance measuring scale to indicate, at spaced positions, the distance apart of the diverging surfaces.

## 39 Citations

A chord diagram expansion coming from some Dyson-Schwinger equations

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We give an expression for the solution to propagator-type Dyson-Schwinger equations with one primitive at 1 loop as an expansion over rooted connected chord diagrams. Along the way we give a…

The signed permutation group on Feynman graphs

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The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to…

Generalized chord diagram expansions of Dyson–Schwinger equations

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Series solutions for a large family of single equation Dyson-Schwinger equations are given as expansions over decorated rooted connected chord diagrams. The analytic input to the new expansions are…

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In this paper, with the study of combinatorial Dyson–Schwinger equations at the level of the universal Hopf algebra of renormalization and with the extension of the universality of this specific Hopf…

On the Enumerative Structures in Quantum Field Theory

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This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected…

Renormalization in connected graded Hopf algebras: an introduction

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- 2010

We give an account of the Connes-Kreimer renormalization in the context of connected graded Hopf algebras. We first explain the Birkho decomposition of characters in the more general context of…

A Lie Theoretic Approach to Renormalization

- Mathematics
- 2007

Motivated by recent work of Connes and Marcolli, based on the Connes–Kreimer approach to renormalization, we augment the latter by a combinatorial, Lie algebraic point of view. Our results rely both…

The combinatorics of Bogoliubov's recursion in renormalization

- Mathematics
- 2007

We describe various combinatorial aspects of the Birkhoff-Connes-Kreimer factorization in perturbative renormalisation. The analog of Bogoliubov's preparation map on the Lie algebra of Feynman graphs…

From Möbius inversion to renormalisation

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- 2020

This paper traces a straight line from classical Mobius inversion to Hopf-algebraic perturbative renormalisation. This line, which is logical but not entirely historical, consists of just a few main…

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