AG Schrader/Schroer Quantum Field Theory and Mathematical Physics

Profile of our Group

The main activities in our group are in the area of Mathematical Physics and Quantum Theory. These activities are integrated in the Sfb 288 (a list of preprints of the Sfb is found here) "Differentialgeometrie und Quantenphysik", in which mathematicians and theoretical physicists from the Technical University Berlin, Humboldt University Berlin and the University of Potsdam participate.

In recent years our main focus has been concentrated on low dimensional quantum field theory, in particular quantum integrable models (including lattice models), conformal and chiral field theories and topological quantum field theories. In particular, we try to understand the new symmetry concepts running under the name of quantum groups, and the new statistics with particle called anyons, and more generally, plektons for which the braid group replaces the permutation group.
The problems require nonperturbative methods, like for example the Bethe ansatz for solving quantum integrable models (the form factor program, initiated here in Berlin and vertex operators techniques) and concepts from algebraic quantum field theory including the modular theory (Tomita-Takesaki theory). Besides quantum field theory we consider modern aspects of Schrödinger operators in quantum mechanics. Thus we consider effects like ionization of atoms by laser pulses. Also we apply methods from scattering theory to the theory of stochastic Schrödinger operators.
Another important long term research program in our group is the inverse problem for periodic Schrödinger operators, i.e. the determination of the potential from the band structure. Closely related is our study of Riemannian surfaces of infinite genus, which leads to new solutions of the KdV equations and might be of interest for string theory.


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