Group Theory in Physics

Course description:
The role of symmetries in physics. Fundamental notions of groups and their linear representations. Schur lemmas. Finite dimensional unitary representations of finite groups: orthogonality and completeness relations for irreducible matrix elements and characters. Regular representation, group algebra. Decomposition of finite dimensional representations of finite groups into irreducible components. Tensor products, Clebsch-Gordan coefficients, tensor operators, Wigner-Eckart theorem. Structure and representation theory of the symmetric group, Young tableaux. Discrete rotation groups and crystallographic point groups. Crystallographic space groups and Bravais lattices. Basic facts on SU(2), SO(3) and GL(n).

Recommended Texts:

• Wu-Ki Tung: Group Theory in Physics, World Sci., Philadelphia, 1985
• Hammermesh M.: Group Theory and its Application to Physical Problems, Dover Publ. Inc., NY 1989
• Naimark M. A., Stern A. I.: Theory of Group Representations, Springer, Berlin, 1982