Code: 02KOHO Cohomological Methods in Theoretical Physics
Lecturer: prof. Ing. Jiří Tolar DrSc. Weekly load: 2 Completion: EX
Department: 14102 Credits: 4 Semester: W
Description:
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.
Contents:
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.
Recommended literature:
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
Keywords:
singular homology, cohomology, associative algebra, Lie algebra, projective representation, deformations of algebras

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