250092 VO C^*-Algebras with Aspects of Quantum Physics (2023W)
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Details
Sprache: Englisch
Prüfungstermine
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
Montag
02.10.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
03.10.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
09.10.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
10.10.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
16.10.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
17.10.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
23.10.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
24.10.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
30.10.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
31.10.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
06.11.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
07.11.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
13.11.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
14.11.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
20.11.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
21.11.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
27.11.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
28.11.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
04.12.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
05.12.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
11.12.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
12.12.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
08.01.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
09.01.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
15.01.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
16.01.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
22.01.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
23.01.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Montag
29.01.
09:45 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Dienstag
30.01.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
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.
Art der Leistungskontrolle und erlaubte Hilfsmittel
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.
Mindestanforderungen und Beurteilungsmaßstab
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.)
Prüfungsstoff
Content of the lecture notes.
Literatur
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.
Zuordnung im Vorlesungsverzeichnis
MANV
Letzte Änderung: Do 23.05.2024 09:46