Universität Wien

250092 VO C^*-Algebras with Aspects of Quantum Physics (2023W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 02.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

C^*-algebras are complex Banach algebras with an involution (*-structure) that is highly compatible with the norm. In view of the most basic models in quantum physics we will focus on C^*-algebras that possess a unit. After a brief review of prerequisites from Banach algebras, we plan to discuss the following topics: Basic theory of C^*-algebras, commutative C^*-algebras, representations of C^*-algebras, von Neumann algebras, the C^*-algebras of canonical commutation and anticommutation relations, quasi-local field algebras.

Ideal prerequisites from functional analysis would be to be familiar with the key concepts as in Chapters I-VII of [C/FA] (see literature) and the spectral theory for bounded self-adjoint operators on a Hilbert space.

Assessment and permitted materials

Oral exam. (In presence or digital.) Scheduling for such (by e-mail) will be available up to one year after the end of this lecture course.

Minimum requirements and assessment criteria

For a successful exam, a thorough understanding of the definitions, results, and proofs has to be shown in detailed answers to questions. (For the discussion of proofs, students may draw on their own notes or the lecture notes.)

Examination topics

Content of the lecture notes.

Reading list

Lecture notes are available at https://www.mat.univie.ac.at/~gue/material.html
Ideal prerequisites from functional analysis would be to be familiar with the key concepts as in Chapters I-VII of [C/FA] and the spectral theory for bounded self-adjoint operators on a Hilbert space. More literature can be found in the lecture notes.

[BR] O. Bratteli and D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics, 2 volumes, Springer-Verlag, 2nd editions 2010 and 1997.

[C/FA] J. B. Conway: A Course in Functional Analysis, Springer-Verlag, 2nd edition 2010.

[C/OT] J. B. Conway: A Course in Operator Theory, American Mathematical Society 2000.

[KR] R. V. Kadison and J. R. Ringrose: Fundamentals of the theory of operator algebras, 2 volumes, Academic Press 1983 and 1986.

[M] G. J. Murphy: C^*-Algebras and Operator Theory, Academic Press 1990.

[T] W. Thirring: Quantum Mathematical Physics: Atoms, Molecules and Large Systems, Springer-Verlag, 2nd edition 2010.

Association in the course directory

MANV

Last modified: Tu 12.11.2024 07:26