Algebra and Dynamics of Quantum Systems (Algebra und Dynamik von Quantensystemen)

Winter term 2017/2018

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Preliminary Program

This lecture aims at students in the programs Mathematical Physics and in Mathematics. It may also be interesting for students in the master program Physics.

If there are international students then the lecture can of course be offered in English. Otherwise the lecture will be in German. The lecture notes will be in English anyway. Please get in contact with me early enough then we can discuss and arrange the details.

The goal of this lecture is to understand the algebras of operators as they occur in quantum mechanics and in quantum field theory models. The important mathematical structure will be a C*-algebra. We will study such algebras in quite some detail together with their representation theory.

Most probably there will be a RiG (research in groups) in the next semester (summer term 2018) based on this course on some more advanced topics in operator algebras.


Some basic knowledge in quantum mechanics will be useful as motivation but even without the course can be taken beneficially. I will assume some familiarity with Banach and Hilbert space theory: here we can discuss what the actual background is and I will adapt the lecture accordingly.


The list of textbooks is rather long, there are many good texts on operator algebras. Many of the references should be seen as background information. At the beginning of the lecture I will point out some more details to particular texts.



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