Universität Wien

260030 VU Topological quantum field theory (2024S)

5.00 ECTS (3.00 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

Donnerstag 07.03. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 14.03. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 21.03. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 11.04. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 25.04. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 02.05. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 16.05. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 23.05. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 06.06. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 13.06. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
Donnerstag 20.06. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 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.

Lecture notes and other supplementary material will be made available.

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 April or May, and one at the end of the term.

Mindestanforderungen und Beurteilungsmaßstab

To formally pass this course, one exercise solution must be made available in written form, a solution to another exercise must be presented in class, and at least 40% of the maximal score in the written test must be obtained. The written test and the exercise solutions will equally contribute to the final grade.

Prüfungsstoff

Content of the lecture course and exercises.

Literatur


Zuordnung im Vorlesungsverzeichnis

M-VAF A 2, M-VAF B

Letzte Änderung: Do 07.03.2024 08:06