UCL - Group theory

[PHY1221]

[22.5h + 15h] 5 credits

This course is taught in the 2d semester.

Teacher(s): Philippe Ruelle

Language: French

Level: First

Aims
Main themes
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

To give a systematic introduction to the theory of groups and their representations, and to demonstrate its usefulness in physics through selected applications.

Main themes

1. Finite groups: fundamental notions and examples ; representations (tensors) ; characters ; tensor products (tensor algebra) ; illustrations on important finite groups (permutations and Young tableaux) ; applications ;
2. Lie groups and Lie algebras: generators ; classical groups ; representations of algebras ; representations of su(2) and tensor products ; lifting to SO(3) ; the su(3) algebra ; representations of linear groups and Young tableaux ; applications.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisites
BAC1 courses in algebra and calculus.