After passing the course the student should be able to: <ul> <li>apply reduction via moment maps to new systems in mechanics and field theory </li> <li>relate the traditional to the modern mathematical formulation of mechanics </li> <li>analyse the role of symmetries in quantum mechanics, quantum field theory and string theory </li> <li>derive supercurrents for a supersymmetric model. </li> </ul>
Symmetries in classical mechanics: The Hamilton funktion. Symplectic geometri. Hamilton flow. Action of Lie groups. Moment maps. Reduction of phase space. Symmetries in quantum mechanics: Wiegners theorem. Representations of the rotation group. Noether currents. Induced representation of Poincare'gruppen. Spinors. Symmetries in quantum field theory: Gaugesymmetries. Supersymmetry. Superspace. Becchi-Rouet-Stora-Tyutin (BRST)-symmetries.. Symmetries in stringteori: Sigmamodels, Duality.
Lectures and seminars with active participation.
Problem assignments possibly with additional oral or written exam.
The course is given as freestanding course and third-cycle course.