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Department of Physics

ΕΛΕ04

10ΕΛΕ04 Group Theory and Applications

Course webpage:  https://eclass.uoa.gr/courses/PHYS299

Course outline

Course content

  • Groups: definition, categories and examples. Multiplication table. Construction of groups. Mapping between groups. Conjugacy classes. Subgroups. Permutation groups. Point symmetry groups.
  • Representations of finite groups. Orthogonality theorems. Character tables. Reducible and irreducible representations. Reduction of representations. Examples from physics. Partial diagonalization in eigenvalue problems using symmetry. Degeneracy. Degeneracy lifting induced by a perturbation.
  • Topological groups and Lie groups. Continuous rotation groups and their representations. The O(2), SO(3), O(3), SU(2) groups. Examples from atomic physics. SU(N) groups with N>2. Young diagrams. Isospin. Nucleon-nucleon scattering.
  • Irreducible tensor operators. Selection rules in optical transitions. Projection operators. Construction of symmetrized eigenfunctions in electronic structure and molecular vibration problems. Crystal harmonics. The group of lattice translations. Bloch theorem.
  • Time reversal symmetry. Kramers degeneracy. Non-unitary groups and their applications in magnetism.