Lecture Event
Dyson--Schwinger equations from Hochschild cohomology
Prof. Dr. Dirk Kreimer (IHES, Frankreich)
8 Apr 2009, 15:00 – 17:00
We first prove locality of counterterms using the Hochschild cohomology of the Hopf algebras introduced in the first lecture. We then show that Dyson-Schwinger equations are solutions of fixed-point equations formulated in this cohomology.
We then study the structure of sub-Hopf algebras and co-ideals. This allows to incorporate the renormalization group so as to turn the Dyson-Schwinger equations into non-linear ordinary differential equations for beta-functions and anomalous dimensions. We study the structure of solutions to these equations. Here, we are mainly interested in non-perturbative results for quanum electrodynamics and quantum chromodynamics.
For further information please have a look at *http://math.bu.edu/people/dkreimer/structure.html*.
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