Cohomological Methods in Theoretical Physics
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 02KOHO | ZK | 4 | 2 | Czech |
- Lecturer:
- Jiří Tolar (gar.)
- Tutor:
- Jiří Tolar (gar.)
- Supervisor:
- Department of Physics
- Synopsis:
-
Singular homology, the de Rham cohomology (quantum mechanics on manifolds). The Čech cohomology and gauge fields. The Chevalley cohomology and projective representations in quantum theory. Deformations of associative and Lie algebras.
- Requirements:
-
02GMF1, 02GMF2
- Syllabus of lectures:
-
1. - 3. Singular homology, de Rham cohomology. Quantum mechanics on manifolds.
4. - 6. Čech cohomology and gauge fields.
7.- 9. Cohomology of Lie algebras. Projective representations in quantum theory.
10. - 12. Deformations of associative and Lie algebras. Quantization as deformation of classical mechanics.
- Syllabus of tutorials:
- Study Objective:
-
Knowledge:
Recognize different types of cohomology.
Skills:
Application of cohomological methods in theoretical physics.
- Study materials:
-
Key references:
[1]B.R. Pollard: An Introduction to Algebraic Topology, Bristol University, 1979
Recommended references:
[2] C. Nash: Topology and physics - a historical essay, arXiv: hep-th/9709135
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans: