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Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
Alain Connes, Dirk Kreimer
This paper gives a complete selfcontained proof of our result announced in hep-th/9909126 showing that renormalization in quantum field theory is a special instance of a general ma…
Renormalization in quantum field theory and the Riemann-Hilbert problem
Alain Connes, Dirk Kreimer
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann-Hi…
Cyclic Cohomology, Hopf Algebras and the Modular Theory
Alain Connes, Henri Moscovici
We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair, consisting of a group-like element and a character, in involution. This provides the key c…
Cyclic cohomology and Hopf algebras
Alain Connes, Henri Moscovici
We show by a direct computation that, for any Hopf algebra with a modulus-like character, the formulas first introduced in [CM] in the context of characteristic classes for actions…
Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries
A. Connes, D. Kreimer
We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned ou…