Seminar “Modern Mathematical Physics”

Date and Time: Tuesday, 9 April 2019, at 2:30 PM

Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics

Seminar topic: “Special Bohr – Sommerfeld geometry and Geometric Quantization”

Speaker: N. A. Tyurin

Abstract:

It was already the 4th time Mathematical Institute SO RAS (Novosibirsk) hosted the international conference “Dynamics in Siberia”. The season for the conference is chosen quite special: at the passing from Siberian winter to spring, when it is not so frozzy while very sunny.

In my talk, I say a few words about the conference, the participants and the talks which were most interesting for me. Then I tell when I have presented at the conference. My talk was devoted to a new construction appeared in the framework of Geometric Quantization of classical mechanical systems with compact phase spaces. There are no global coordinates in this case so the method of Canonical quantization does not work; despite of this one knows two major approaches, which can be applied in the absolutely general situation. The first one exploits the prequantization data, and the corresponding Hilbert space is given by the smooth section space for the prequantization bundle. On the other side, the Lagrangian approach is based on the considerations of so-called Bohr – Sommerfeld lagrangian cycles in the phase space. One establishes that both the approaches can be unified in the framework of Special Bohr – Sommerfeld geometry.

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