Website of the course "Group theory for physicists", WS 2025/26

• 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


• Time and place
• Lecture: Tu 12-14 and Fr 12-14 in H33 (first lecture on Oct. 14)
• Exercises: Mo 14-16 in 5.0.20
• Please register for the exercises (52449) so that I can contact you by email.
  Unfortunately the registration is only open until Oct. 16 (23:59). 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 on October 20
• Problem set 2 for the exercises on October 27
• Problem set 3 for the exercises on November 3
• Problem set 4 for the exercises on November 10


• 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"