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.

Syllabus:

-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