**PH-701 Group Theory **

- Finite Groups
**:**groups and representations, the regular representations, irreducible representations, transformation groups and applications, Schur’s lemma, orthogonality relations, characters, eigenstates, tensor products. - Lie groups
**:**generators, Lie algebras, Jacobi identity, the adjoint representation, simple algebras and groups, states and operators. - SU(2): eigenstates of J3, raising and lowering operators, tensor products.
- Tensor operators: orbital angular momentum, Wigner Eckart theorem and examples, product of tensor operators.
- Isospin: charge independence, creation operator, number operators, isospin generators, symmetry of tensor products, the deuteron, superselection rules.
- Roots , weights and SU(3): Gellmann matrices, weights and roots of su(3), positive weights, simple roots, constructing the algebra, Dynkin diagrams and examples, the Cartan matrix, the trace of generator, fundamental representation of SU(3), constructing the states, the Weyl group, complex conjugation and example of other representation.
- Tensor method:
- Hypercharge and strangeness
**:**the eight-fold way, the Gellmann-Okubo formula, hadron resonances, quarks. - Young tableaux and SU(n): raising and lowering indices, Clebsch-Gordan decomposition, U(1), generalization of gell-mann matrices, SU(N) tensors, dimensions, complex representations
- The Lorentz and Poincare groups and space-time symmetries:

**Recommended Texts**

*Lie algebras in Particle Physics: From Isospin to Unified Theories,*Westview Press; 2nd edition, 1999.*Group Theory in Physics*, Wu-Ki-Tong, World Scientific, 1985.