Walter van Suijlekom
(Radboud U Nijmegen)
Hopf algebras of Green's functions in perturbative quantum field theory
We present a new result on the existence of Hopf subalgebras in the Hopf
algebra of Feynman graphs, which are generated by 1PI Green's functions.
This means that the coproduct closes on these Green's functions which
allows us for example to rederive Dyson's formula in QED relating the
renormalized and unrenormalized proper functions via the renormalization
constants. In the case of non-abelian gauge theories, we observe the
crucial role played by Slavnov-Taylor identities.
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