250092 VO C^*-Algebras with Aspects of Quantum Physics (2023W)
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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.
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: Th 11.04.2024 14:46