Symmetry and conservation laws
Groups and group representations
Point groups
Permutation Groups
Lie Groups and Lie Algebras
Unitary Groups
Real Orthogonal Groups
The Symplectic Groups
Theory of identical particles
Angular momentum
SU(N) group in nuclear and particle physics
Coefficient of fractional parentage and seniority
Isospin symmetry
Spin and pseudospin symmetry in nuclear and relativistic systems
The main aim of the course is to understand the basic concepts in symmetry principles and group theories and their mathematical formalisms. On completion of the course, the students will be able to apply them to analyze the symmetry properties of complex quantum physical systems including atoms, nuclei and elementary particles. They should also be able to analyse both discrete and continuous symmetries of physical systems using group theory. In particular they should be able to decompose a representation into its irreducible representations. The students will also be able to identify approximate symmetries including isospin and pseudospin and understand their limitations.