Multiplicative renormalization and Hopf algebras

Details Multiplicative renormalization and Hopf algebras Multiplicative renormalization and Hopf algebras

2007-07-04

arxiv.org/abs/0707.0555v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages; uses feynmp

Scientific paper

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.

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