Multiplicative Renormalization and Hopf Algebras

  • Walter D. van Suijlekom
Part of the Progress in Mathematics book series (PM, volume 279)


We derive the existence of Hopf subalgebras generated by Green’s functions in the Hopf algebra of Feynman graphs of a quantum field theory. This means that the coproduct closes on these Green’s functions. It allows us for example to derive Dyson’s formulas in quantum electrodynamics relating the renormalized and bare proper functions via the renormalization constants and the analogous formulas for non-abelian gauge theories. In the latter case, we observe the crucial role played by Slavnov–Taylor identities.


Hopf Algebra Ward Identity Feynman Graph Renormalization Constant Hopf Subalgebra 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute for Mathematics, Astrophysics and Particle Physics Faculty of ScienceRadboud Universiteit NijmegenNijmegenThe Netherlands

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