Ort: 1090 Wien
Straße: Boltzmanngasse 5
For past teaching see the u:find-page
In order to cure the old problems of quantum field theory (infrared and ultraviolet divergences as well as the divergence of the renormalized pertubation expansion), one was led to the formulation and study of models over deformed space-time, taking into account certain gravity effects. Noncommutative Geometry provides themathematical framework and gives interesting regularization methods.
The main focus concerns the renormalization problems and the questions of nonperturbative construction of quantum field theory models.
The problem of renormalization suffers form the IR/UV mixing. The first way to solve it has been found in common work with Raimar Wulkenhaar. This model leads to a taming of the Landau ghost, the beta-function vanishes and a new nontrivial fixed point shows up. The model is asymptotic safe. This led to the first nontrivial 4 dimensional model which has recently been constructed by us nonperturbatively. Greens-functions are given by solvable integral equations.
This technique will be applied to various models in order to learn about general aspects. Especially noncommutative gauge model are studied together with Daniel Blaschke and collaborators. Fermion models have been studied too.
What concerns the principles of nc QFT over deformed Minkowski space-time we (together with Gandalf Lechner) found a way to implement Lorentz symmetry, but locality turns into localization of fields in wedges. This promising direction will be followed, especially the connection of the Euclidean framework to the Minkowski one is discussed. If we deform only two directions of the four dimensional space, we found a way to connect both formulations.