826 citations · 3.9k across the 91 of their papers we have counts for
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hep-th2000★ 47 cited
Combinatorics of (perturbative) quantum field theory
Dirk Kreimer
We review the structures imposed on perturbative QFT by the fact that its Feynman diagrams provide Hopf and Lie algebras. We emphasize the role which the Hopf algebra plays in reno…
hep-th2000★ 8 cited
Feynman diagrams and polylogarithms: shuffles and pentagons
Dirk Kreimer
We summarize the Hopf algebra structure on Feynman diagrams and emphasize the interest in further algebraic structures hidden in Feynman graphs.
hep-th2000★ 318 cited
Renormalization in quantum field theory and the Riemann-Hilbert problem II: the -function, diffeomorphisms and the renormalization group
Alain Connes, Dirk Kreimer
We showed in part I (hep-th/9912092) that the Hopf algebra of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group …