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Instructors: H.Panagopoulos, N.Toumbas 

Content: 

Symmetries: Definition. Physical consequences of symmetries. Symmetries in Classical Mechanics, Discrete/continuous symmetries, Local/global symmetries.
Finite groups: Reducible representations, Characters, Schur's lemma, Tensor product, Permutation groups, Young tableaux.
Crystallographic groups, Brillouin zones in crystals, Atomic energy level splitting.
Continuous groups: Lie groups, Lie algebras.
Rotation group: Representations in Classical Mechanics. Angular momentum in Quantum Mechanics. Clebsch-Gordan coefficients. Lorentz group and its spinorial representations.
Roots and weights: Dynkin diagrams. Classification of classical groups.
SU(N) groups in Particle Physics: Isospin, Hypercharge, Hadronic spectrum. Model building for Grand Unified Theories.
Supersymmetry: Supersymmetric algebras and groups. Applications to the Supersymmetric Standard Model and to Supergravity.
Infinite dimensional algebras: Virasoro algebra, Kac-Moody algebras. Applications to Conformal Field Theories, and to String Theory.
 

Assesment:  Homework sets: 10%,  Class presentations: 40%,  Final exam: 50%.