Fri, 03.11.2017, 15:45 |
Operator algebras, order, and semigroups Mathematisches KolloquiumSpeaker:
Prof. Dr. Karl-Hermann Neeb, Universität Erlangen-NürnbergRoom:
S2|08 /171 (Uhrturm)
Operator algebras, order and semigroups have been core themes of Karl Hofmann's mathematical work at different times of his life. Here we discuss some current problems at the borderline between mathematics and quantum physics, where these themes play a central role. \\ Concretely, we are interested in the space $Stand(H)$ of so-called standard subspaces of a complex Hilbert space $H$. These are closed real subspaces $V\subseteq H$ satisfying $V \cap i V = \{0\}$ and $\overline{V+ i V} = H$. In Quantum Field Theory standard subspaces encode crucial information on nets of algebras of local observables, but they are much easier to deal with than the operator algebras themselves. Nevertheless they contain most of the information on symmetries. Here a good understanding of the structure of the inclusion order on $Stand(H)$ is an important problem. On possible approach is based on antiunitary representations of finite dimensional Lie groups $G$ on $H$ and the structural information on the subsemigroup $S_V := \{g \in G \: gV \subseteq V\}$. |
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Fachbereich Mathematik

Technische Universität Darmstadt

Schlossgartenstraße 7

64289 Darmstadt