PHYS515 GROUP REPRESENTATIONS
| Course Code: | 2300515 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Physics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | |
| Offered Semester: | Once in several years. |
Course Objectives
Students will acquire the basic knowledge of
- theory of finite groups and their representations
- theory of Lie algebras and Lie groups and their representations
- Cartan-Weyl methods to develop the representation theory of classical Lie algebras
- Cartan classification of classical groups and the Dynkin diagrams
- Elementary methods for tensor products of representations. Basic examples in elementary particle physics.
- Theory of the Lorentz Group and its uses in Physics
Course Content
Lie groups. Lie algebras. Symmetry groups of differential equations. Invariant forms on Lie groups. Ideals, solvability and nilpotency. Cartan subalgebras and root spaces. Coxeter-Dynkin diagrams. Classical Lie algebras. Representation theory. Tensor products. Enveloping algebras and Casimir operators. Physical applications.
Course Learning Outcomes
The students will gain knowledge on the conceptual foundations of the theory of finite and continous groups. They will acquire the fundamental and some advanced technical skills in using Lie algebras and Lie groups and applying them as a mathematical tool in physical applications.