Wave-Function renormalization and the Hopf algebra of Connes and Kreimer

Abstract

In this talk, we show how the Connes-Kreimer Hopf algebra morphism can be extended when taking into account the wave-function renormalization. This leads us to a semi-direct product of invertible power series by formal diffeomorphisms.

5 pages, no figure, talk presented in the conference "Brane New World and Noncommutative Geometry", Torino, Villa Gualino,(Italy) October

References in corpus (2)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group

Cited by in corpus (6)

• Combinatorial Hopf algebras in quantum field theory I
• Hopf algebra approach to Feynman diagram calculations
• Combinatorics of (perturbative) quantum field theory
• The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras
• An algebraic Birkhoff decomposition for the continuous renormalization group
• The interface of noncommutative geometry and physics