The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras

Understand

We study the structure of renormalization Hopf algebras of gauge theories.

• We identify certain Hopf subalgebras in them, whose character groups are semidirect products of invertible formal power series with formal diffeomorphisms.
• This can be understood physically as wave function renormalization and renormalization of the coupling constants, respectively.
• After taking into account the Slavnov-Taylor identities for the couplings as generators of a Hopf ideal, we find Hopf subalgebras in the corresponding quotient as well.