Department Mathematik
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Somersemester 2022

Seminar: Geometric Quantization

Prof. Dr. Martin Schottenloher

Mo 16-18, HS B 132, hybrid. Beginn: 28.04.22
Information about the Lecture Notes: See below!

Schedule

  • 28.04.2022 Vorbesprechung
  • 05.05.2022 fällt aus
  • 09.05.2022 Quantisation of the Kepler problem (Felix Physiker)
  • 16.05.2022 fällt aus
  • 23.05.2022 Orbit Method: Unitary Representations and History of Geometric Quantization (Lehel Csillag)
  • 30.05.2022 Quantum Geometric Langlands (Robert Windesheim)
  • 06.06.2022 fällt aus; Pfingsten
  • 13.06.2022 ausgefallen
  • 20.06.2022 Half-density Quantization (T. Patuleanu)
  • 27.06.2022 Half-form Ouantization (L. Csillag)
  • 04.07.2022 Bohr-Sommerfeld Condition (Nicky Sadhigi)
  • 11.07.2022
  • 18.07.2022
  • 25.07.2022
  • 01.08.2022 Borel-Weil for Polarizations (Xumin Liang)
Planned
  • Chern-Simons Theory I (Philipp Bakauov)
  • Chern-Simons Theory II (Philipp Bakauov)
  • Berezin-Toeplitz Quantization (Aditya Basu)
  • Cohomological obstructions to lifting the symplectic action to a Hamiltonian action (Tudor Patuleanu)

The objective of the seminar is to complement the course on "Geometric Quantization" of the last semester. In particular in connection with the following subjects

  • Prequantization and integrality conditions
  • Cohomology
  • The holomorphic case and Kähler manifolds
  • Geometry of polarisations
  • Half-density quantization
  • Half-form Quantization
  • Metaplectic correction
  • Coadjoint orbits
  • Quantization of Chern-Simons-theory
  • Reduction and Quantization
  • Other quantization schemes
Also: Detailed Examples are highly welcome! Bibliography:

  • S. Bates and A. Weinstein, Lectures on the geometry of quantization, Berkeley Mathematics Lecture Notes 8, AMS (1997).
  • J.-L. Brylinski, Loop Spaces, characteristic classes, and geometric quantization (1993), Birkhäuser-Verlag.
  • N.E. Hurt, Geometric Quantization in Action (1982), Reidel Company.
  • Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lecture Notes in Math. 170, p. 87-208, 1970.
  • M. Puta, Hamiltonian Mechanical Systems and Geometric Quantization (1993), Kluwer Publications.
  • J. Sniaticky, Geometric Quantization and Quantum Mechanics (1980) Springer-Verlag.
  • Nicholas Woodhouse, Geometric quantization (1980) Oxford University Press.

Für:

Interested students of physics or of mathematics.
If you plan to participate, please contact me (martin@schottenloher.de).

Information about the Course 21/22

Here are the Lecture Notes about the Course of the last semester. They are still in development. They will be updated frequently. The changes from version to version are reported in Status and Changes.
The folder of Exercises.
The plan of the course formulated in August 2022.