Group Theory methods in Physics

This group theory course is pitched at beginners at UG/PG levelso that the students can appreciate the wide applications of the group theory tools in other areas of physics.INTENDED AUDIENCE : Physics backgroundPREREQUISITES : Linear algebra, quantum mechanics, special theory of relativityINDUSTRY SUPPORT :This tool may be applicable at R&D department of industries

Syllabus

Week 1 : Introduction to discrete groups, subgroups and generators, conjugacy classesWeek 2 : Symmetric groups, permutation group, cycle notationWeek 3 : Direct product groups, semi-direct product groupsWeek 4 : Symmetries of molecules, point groups and stereographic projectionWeek 5 : Matrix representation of groups, reducible and irreducible representationWeek 6 : Great orthogonality theorem and character tables, Mulliken notation, basisWeek 7 : Tensor product, projection operator, observables, selection rules, molecular vibrationsWeek 8 : Continuous groups, generators, Lorentz transformationWeek 9 : Orthogonal groups and Lie algebraWeek 10 : Unitary groups, SU(2), SU(3), weight vector diagrams and root vector diagramsWeek 11 : Wigner-Eckart theorem, examplesWeek 12 : Quark model, SU(3) baryons, mesons, Wigner-Eckart theorem, hydrogen atom, dynamical symmetry