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Abstract

The preservation of gauge symmetries to the quantum level induces symmetries
between renormalized Green's functions. These symmetries are known by the names
of Ward-Takahashi and Slavnov-Taylor identities. On a perturbative level, these
symmetries can be implemented as Hopf ideals in the Connes-Kreimer
renormalization Hopf algebra. In this article, we generalize the existing
literature to the most general case by first motivating these symmetries on a
generic level and then proving that they indeed generate Hopf ideals, where we
also include the more involved cases of super- and non-renormalizable local
QFTs. Finally, we provide a criterion for their validity on the level of
renormalized Feynman rules.