### The Manifold Geometries of QFT, II (Suijlekom on Renormalization, Hopf Algebra and BV-Formalism)

#### Posted by Urs Schreiber

The highlight of today’s talks at The manifold geometries of QFT for me was a talk by Walter v. Suijlekom in which he made a connection between the Connes-Kreimer Hopf algebra of Feynman diagrams and the BV-formalism.

Building on the Connes-Kreimer fact that Feynman diagrams form a Hopf algebra, there is a certain Hopf quotient which one can form. The question is what this corresponds to physically. The answer Walter Suijlekom gives is: it corresponds to imposing the BV master equation!

I have taken rather detailed notes, with everything that was on the blackboard, here. For everything except the BV-stuff and relations to it look at his latest very readable article

Walter D. van Suijlekom
*Renormalization of gauge fields using Hopf algebras*

arXiv:0801.3170

## Re: The Manifold Geometries of QFT, II (Suijlekom on Renormalization, Hopf Algebra and BV-Formalism)

I look forward to the grand day when I will be able to understand this. So many pieces of the puzzle seem to be clicking into each other now. It’s like that mysterious point in a statistical mechanical system when the “correlations go to infinity”, or like in Back to the Future, where we are approaching 88 miles per hour and lightning is going to blast down from the church tower any moment now and blast us into the future!