AG Schrader/Schroer | Quantum Field Theory and Mathematical Physics |
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.