Physics – Mathematical Physics
Scientific paper
2008-07-07
Physics
Mathematical Physics
30 pages; minor corrections, to appear in CMP
Scientific paper
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. In the second part of the paper, we explain the origin of these Hopf ideals by considering a coaction of the renormalization Hopf algebras on the Batalin-Vilkovisky (BV) algebras generated by the fields and couplings constants. The so-called classical master equation satisfied by the action in the BV-algebra implies the existence of the above Hopf ideals in the renormalization Hopf algebra. Finally, we exemplify our construction by applying it to Yang-Mills gauge theory.
No associations
LandOfFree
The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-561265