Cohomological Methods in Theoretical Physics

Lecturer:

Jan Vysoký

Tutor:

Supervisor:

Department of Physics

Synopsis:

Singular homology, the de Rham cohomology. 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. Singular homology

2. de Rham cohomology

3. Čech cohomology and gauge fields.

4. Cohomology of Lie algebras

5. Projective representations in quantum theory

6. Deformations of associative and Lie algebras

7. Quantization as deformation of classical mechanics.

Syllabus of tutorials:

Exercises involve concrete examples of application of cohomological methods in theoretical physics as home work.

Study Objective:

Knowledge:

The students get to know various types of cohomology applicablie in theoretical physics.

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 2020/2021:

Time-table is not available yet

Time-table for summer semester 2020/2021:

Time-table is not available yet

The course is a part of the following study plans:

• Matematická fyzika (compulsory course of the specialization)