Universität Wien FIND

260081 VU Topological quantum field theory (2022W)

6.00 ECTS (4.00 SWS), SPL 26 - Physik
Prüfungsimmanente Lehrveranstaltung

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 15 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

Dienstag 11.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 13.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 18.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 20.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 25.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 27.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 03.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 08.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 10.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 15.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 17.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 22.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 24.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 29.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 01.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 13.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 15.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 10.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 12.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 17.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Donnerstag 19.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Dienstag 24.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

This course is an introduction to an axiomatic, functorial approach to topological quantum field theory (TQFT). In physics, TQFT offers a rigorous and (arguably) elegant framework to study and develop some aspects of quantum field theory in general, and to describe specific phases of matter and models of topological quantum computation in particular. Mathematically, TQFT provides algebraic invariants of manifolds (often with extra structure such as orientation, spin, or knots).

We will start with a concise review of (desired) properties of path integrals, and explain how they motivate the axiomatic definition of TQFTs in terms of monoidal categories and functors. These and related notions will be introduced (with no special prior knowledge assumed), along with various illustrating examples. Some of the general theory of TQFTs in arbitrary "spacetime" dimension d will be developed. After that we will mostly consider the cases d=2 (related to string theory and conformal field theory) and d=3 (related to topological phases of matter and quantum computation). In particular, we will study "state sum models" and "sigma models".

Prerequisites: Familiarity with linear algebra, some basic ideas about quantum physics, a fondness for algebraic structures, and a mere interest in the functorial approach to quantum field theory (the relevant notions and theory of categories and functors will be introduced from scratch in the lecture). Physicists and mathematicians are equally welcome to participate.

If in-person classes are not an option because of the COVID-19 pandemic, lectures and exercise classes will be held online (via BigBlueButton or similar free and open software) synchronously. Optional discussion sessions will be offered on a regular basis, and questions and other feedback are encouraged also by messenger or email. Lecture notes and other supplementary material will be made availble.

UPDATE (in mid-September): The course will start in on-site mode on October 11. Participants are encouraged to let the lecturer know if/when they prefer on-site or online lectures.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Questions and comments during and after the lectures are encouraged, regular attendance is recommended. To get credits for this course, students will be asked to present their solutions for at least one exercise, and participate in two written tests, one in December and one at the end of the term.

Mindestanforderungen und Beurteilungsmaßstab

To formally pass this course, one exercise solution must be presented, and at least 50% of the combined maximal score in the two written tests must be obtained. The written tests will each contribute ⅓ to the final mark, the exercise presentation will contribute another ⅓.

Prüfungsstoff

Content of the lecture course and exercises.

Literatur


Zuordnung im Vorlesungsverzeichnis

M-ERG

Letzte Änderung: Mi 14.09.2022 15:49