Universität Wien

260081 VU Topological quantum field theory (2022W)

6.00 ECTS (4.00 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

  • Tuesday 11.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 13.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 18.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 20.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 25.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 27.10. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 03.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 08.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 10.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 15.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 17.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 22.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 24.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 29.11. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 01.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 06.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 13.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 15.12. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 10.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 12.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 17.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 19.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 24.01. 11:15 - 12:45 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 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.

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.

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 December and one at the end of the term.

Minimum requirements and assessment criteria

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.

Examination topics

Content of the lecture course and exercises.

Reading list

Association in the course directory

M-ERG

Last modified: We 14.09.2022 15:49