Universität Wien
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260030 VU Topological quantum field theory (2024S)

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Continuous assessment of course work
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 15 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 07.03. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 14.03. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 21.03. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 11.04. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 18.04. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 25.04. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 02.05. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 16.05. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 23.05. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 06.06. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 13.06. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 20.06. 10:30 - 13:00 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien

Information

Aims, contents and method of the course

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.

Assessment and permitted materials

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.

Minimum requirements and assessment criteria

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

Examination topics

Content of the lecture course and exercises.

Reading list

Association in the course directory

M-VAF A 2, M-VAF B

Last modified: We 12.06.2024 19:46