Cohomological Methods in Theoretical Physics

Course guarantor:

Lecturer:

Tutor:

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: