Title of the course: Symplectic geometry and dynamics on group manifolds
Instructor: Prof. George Jorjadze
Institution: Free University of Tbilisi, Razmadze Mathematical Institute of TSU
Dates: 18-26 September 2017
Prerequisites: Classical and quantum mechanics, field theory, elements of group theory
Level: Graduate, advanced undergraduate
Lecture 1. Review of Lagrangian and Hamiltonian dynamics;
First Noether theorem;
Gauge invariant systems and second Noether theorem;
Lecture 2. Elements of differential geometry;
Generalized Hamiltonian dynamics;
Symplectic structure on the space of solutions.
Lecture 3. Lie algebras, Killing form;
Exponential map and Lie groups;
Group manifolds, vector fields and 1-forms;
Moment map, co-cycles of Lie algebras.
Lecture 4. Liouville model;
Free particle in a curved space;
Particle dynamics on a group manifold;
Particle dynamics on AdS and dS spaces.
Lecture 5. Free field theory on a cylinder;
Chiral symplectic forms;
Coset WZW models.
Lecture 6. Solution of exercises and problems.