The course gives an introduction to symmetry groups in physics. It explains the relevant mathematical background (finite groups, Lie groups and algebras as well as their representations), and illustrates their important role in modern physics.

Learning objective

The aim of the course is to give a self-contained introduction into finite group theory as well as Lie theory from a physicists point of view. Abstract mathematical constructions will be illustrated with examples from physics.

Content

symmetries in two and three dimensions, groups and representations, finite group theory, point and space groups, structure of simple Lie algebras, finite-dimensional representations; advanced topics such as: representations of SU(N), classification of simple Lie algebras, conformal symmetry