Symmetry in Physics

10 credits

Syllabus, Master's level, 1FA158

A revised version of the syllabus is available.

Code: 1FA158
Education cycle: Second cycle
Main field(s) of study and in-depth level: Physics A1F
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 18 March 2010
Responsible department: Department of Physics and Astronomy

Entry requirements

120 credits with Analytical Mechanics and Special Relativity Theory or similar.

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.