In­for­ma­ti­on on the Em­my-Noe­ther Pro­ject

Quantengeometrie: Mathematische Physik auf dem Weg zur Quantengravitation

(Quantum Geometry: Mathematical Physics along the road to Quantum Gravity)

Coordinates

The group was funded by the Emmy-Noether-Programm of the Deutsche Forschungsgemeinschaft under grant FL 622/1-1 from August 2006 until November 2013. Since November 2009, the group had been affiliated to the Mathematics Department of Paderborn University. Before, until October 2009, the group had been affiliated to the Center for Mathematical Physics and to the Analysis and Differential Geometry Division of the Mathematics Department at Hamburg University.

Short Summary

The unification of quantum theory and gravitation is one of the most important unsolved problems of modern physics. In particular, due to the lack of experimental data, it is crucial to investigate this issue mathematically. Currently, there are three major approaches to attack this problem: loop quantum gravity, noncommutative geometry, and string theory. The proposed project is devoted to quantum geometry, being a main point of the first mentioned area. At the same time, we strive for an exchange of ideas and methods with algebraic quantum field theory, being closely related to noncommutative geometry, and hope to connect both fields this way.

Within the project we are going to investigate, how far the quantization of classical theories may be unique or whether superselection sectors may arise. Here, the presence of symmetries will play a crucial role. At the same time, we are going to study what highly symmetric models (as known, e.g., from quantum cosmology) can tell us about the full, but still unknown theory of quantum gravity. Finally, global covariance of gravity should be treated in a mathematically adequate way and without separation of space and time. The necessary mathematical methods will mainly come from analysis (global and functional analysis) and geometry (differential and algebraic geometry).