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.

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

Finite group theory, including representation theory and character methods; application to crystal field splitting. The symmetric group and the structure of its representations; application to identical particles and parastatistics. Simple Lie algebras and their finite-dimensional representations. Description of representations of SU(N) in terms of Young diagrams; applications in particle physics.