Renormalization as an Algebraic Birkhoff Decomposition

15.10.2021, 11:00  –  Golm, Haus 9, Raum 2.22 und online
Arbeitsgruppenseminar Analysis

David Prinz (University of Potsdam)

In this talk, I will give an introduction to renormalization theory in the framework of Connes and Kreimer. To this end, I will start with a brief introduction to perturbative Quantum Field Theory. This will lead us to divergent integral expressions, called Feynman integrals. In order to produce probabilities for physical processes, they need to be manipulated in a certain way, called renormalization. It was realized by Kreimer (1998) that the subdivergence structure of these Feynman integrals can be organised via a Hopf algebra of graphs. In this approach, Feynman integrals are considered as characters (i.e. algebra morphisms) from this Hopf algebra to an appropriate target algebra. Subsequently, together with Connes (1999), they formulated the renormalization of these characters as an algebraic Birkhoff decomposition. Using these techniques, I will then explain in my follow-up talk on October 22 how the famous renormalization problem of General Relativity could be resolved via an infinite tower of Ward identities.

Let me also take this opportunity to mention forthcoming talks on October 22nd (tentative title: Hopf Ideals for General Relativity),by Marija Dimitrijevic Ciric (University of Belgrad, Serbia) on October 29th, by Rosa Preiss (University of Potsdam) on November 5th, by Claudio Diappiaggi (University of Pavia, Italy) on November 26th, and by Yannic Vargas (Unievrsity of Potsdam) on December 3rd.

For those of you who can and would like to join us, please meet us in the seminar Room 2.22 of the maths institute, where we can follow the talk together on screen.

You are welcome to invite your friends and colleagues to join us! If you wish to attend the talks,  please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.