Group Theory methods in Physics

Week 1 : Introduction to discrete groups, subgroups and generators, conjugacy classes

Week 2 : Symmetric groups, permutation group, cycle notation

Week 3 : Direct product groups, semi-direct product groups

Week 4 : Symmetries of molecules, point groups and stereographic projection

Week 5 : Matrix representation of groups, reducible and irreducible representation

Week 6 : Great orthogonality theorem and character tables, Mulliken notation, basis

Week 7 : Tensor product, projection operator, observables, selection rules, molecular vibrations

Week 8 : Continuous groups, generators, Lorentz transformation

Week 9 : Orthogonal groups and Lie algebra

Week 10 : Unitary groups, SU(2), SU(3), weight vector diagrams and root vector diagrams

Week 11 : Wigner-Eckart theorem, examples

Week 12 : Quark model, SU(3) baryons, mesons, Wigner-Eckart theorem, hydrogen atom, dynamical symmetry