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Information on the Emmy-Noether Project

Quantengeometrie: Mathematische Physik auf dem Weg zur Quantengravitation
(Quantum Geometry: Mathematical Physics along the road to Quantum Gravity)


The group is affiliated to the Center for Mathematical Physics and the Analysis and Differential Geometry Division of the Mathematics Department at Hamburg University.
The starting date was August 2006.

Group members

Christian Fleischhack
Johannes Brunnemann

Ph.D. student:
Diana Kaminski

Former Group Member

Ph.D. student:
Heiko Remling
(from August 2006 until March 2007; now Technical University of Clausthal)

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).
Last modified: Apr 1, 2007 by Christian Fleischhack