On completion of the course, the student should be able to
apply symmetry considerations and group theory to solve problem within molecular physics, solid state physics and particle physics
analyse both discrete and continuous symmetries of physical systems using group theoretical tools
analyse properties of physical systems, such as transition probabilities, by means of representations
use Young tableaux, Clebsch-Gordan decomposition and Wigner-Eckart theorem in calculations
apply representation theory and decompose into irreducible representations
calculate Casimir operators for Lie groups, construct their root and weight diagrams and calculate roots and weights
The course gives a general introduction to the description of symmetry properties of physical systems. Group theory and the theory of group representations. The Wigner-Eckart theorem. Young tableaux. Discrete groups: point groups, space groups and the permutation group with applications within molecular and solid state physics. Continuous groups and Lie algebra with applications within particle physics, such as the special unitary groups and the Lorentz and Poincaré the groups. General treatment of Lie groups.