Lie groups in physics.
The aim of this course is to give an introduction into the theory of Lie groups, Lie algebras, and their representations, with a special emphasis on applications in physics. The focus will be on actual computations, therefore some of the mathematical theorems will not be rigorously proven, only motivated and illustrated.
-Introduction, examples for continuous groups (rotation group, gauge groups, coordinate transformations, etc.)
-Definitions: Lie groups, Lie algebras, simplex examples
-Representations: definitions, main statements, Clebsch-Gordan series
-Irreducible representations of SU(2), tensor method, algebraic method
-Irreducible representations of SU(3)
-Representations of SU(N) and GL(N) with the tensor method, Young diagrams
-Classification of simple Lie algebras (Cartan generators, Killing form, Dynkin diagrams)
-Representations of simple Lie algebras