**General information**- Lecturer: Prof. Tilo Wettig
- 4 hours lecture + 2 hours exercises
- Special course in physics (Bachelor or Master), 8 ECTS points
- Pass/fail only, passing determined by active participation in the exercises (see below)
- Language: English (unless everyone wants it to be in German)
**Time and place**- Lecture: Tu 12-14 and Fr 12-14 in H33 (first lecture on Oct. 18)
- Exercises: Mo 14-16 in 5.0.20 and Tu 8-10 in 5.0.21
- Please register for the exercises (52449) so that I can contact you by email.

Unfortunately the registration is only open until Oct. 20. If you missed this date please send me an email. - Office hours: after the lecture, by appointment, or without appointment in my office (PHY 4.1.10)
**Problem sets**- Problem set 1 for the exercises in the week of October 24
- Problem set 2 for the exercises in the week of October 31
- Problem set 3 for the exercises in the week of November 7
- Problem set 4 for the exercises in the week of November 14
- Problem set 5 for the exercises in the week of November 21
- Problem set 6 for the exercises in the week of November 28
- Problem set 7 for the exercises in the week of December 5
- Problem set 8 for the exercises in the week of December 12
- Problem set 9 for the exercises in the week of December 19
- Problem set 10 for the exercises in the week of January 9
- Problem set 11 for the exercises in the week of January 16
- Problem set 12 for the exercises in the week of January 23
- Problem set 13 for the exercises in the week of January 30
- Problem set 14 for the exercises in the week of February 6
**Contents of the course** Group theory plays an
essential role in physics, in particular for the description of
phenomena based on symmetries. However, typically only a few
physicists benefit from a systematic education in group theory. The
course tries to partially close this gap. After an introduction
to the basics of group theory we will discuss important applications
in physics.
- Mathematical foundations
- finite groups
- subgroups, classes, cosets, etc.
- morphisms
- representation theory
- irreducible tensors and Wigner-Eckart theorem
- Lie groups
- construction of irreducible representations
- and others
- Applications in physics
- symmetries and degeneracies in quantum mechanics
- classification of eigenstates, selection rules
- hydrogen atom
- SU(2) and SU(3) in particle physics
- spontaneous symmetry breaking and Goldstone theorem
- elementary particles and irreducible representations of the Poincaré group
- and others
**Prerequisites**- Analysis, Linear Algebra, physics courses up to Quantum Mechanics I
- No prior knowledge of group theory required.
**Rules for the exercises:**
To really understand the material it is essential to solve the
problems. Therefore you should try to work them out yourselves. To
motivate you to do so the following rules hold:
- You do not have to hand in written solutions to the exercises, but you have to be able to present the solutions.
- At the beginning of each exercise session you check which problems you are prepared to present. The presenter will be chosen at random.
- In order to pass the course, you have to check at least 50% of all problems over the course of the semester.
- If you cannot present a problem even though you have checked it you get a minus point, with the following consequences:
- You can afford a single minus point.
- With two minus points you need to pass an oral exam to pass the course.
- With three minus points you fail the course.
- You are welcome to discuss the problems with other students but should make sure that you really understand the solutions.
**Literature**- I.V. Schensted, "A course on the applications of group theory to quantum mechanics"
- W.-K. Tung, "Group theory in physics"
- M. Tinkham, "Group theory and quantum mechanics"
- H. Boerner, "Darstellungen von Gruppen"
- R. Gilmore, "Lie groups, Physics, and Geometry"
- H.F. Jones, "Groups, representations and physics"
- J.F. Cornwell, "Group theory in physics"
- S. Sternberg, "Group theory and physics"
- R. Gilmore, "Lie groups, Lie algebras, and some of their applications"
- D.B. Želobenko, "Compact Lie groups and their representations"