Omschrijving |
Symmetry plays an important role in the description of physical systems. Group theory is a way to treat symmetry systematically. The course starts with the theory of abstract groups, after which the topic of representations will be treated. The lectures will focus on groups of relevance for physics, such as symmetry groups of molecules and crystals (point and space groups), permutation groups, orthogonal and unitary groups, Euclidean, Lorentz and Poincaré groups. Applications of group theory in physics, especially in quantum mechanics, will be given throughout the course. Specific subjects to be covered include: groups, subgroups, conjugacy classes, isometries, homomorphisms, isomorphisms, irreducible representations, Schur's lemmas, characters, character tables, invariant vectors and tensors, symmetry breaking and lifting of degeneracy, tensor product representations, Clebsch-Gordan decompositions, transformations of wave functions and operators, and some aspects of Lie groups and Lie algebras. |