Group Theory in Physics

Module PH2116

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2116 is a semester module in German or English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 75 h 5 CP

Responsible coordinator of the module PH2116 is Norbert Kaiser.

Content, Learning Outcome and Preconditions


Basic notions for groups, cyclic groups, classification of finitely generated abelian groups, permutation groups, group actions, Sylow theorems, finite rotation groups in 3d, definition a Lie group, orthogonal and unitary groups, SO(3) is not simply connected, spin groups, quaternions, Lorentz group and its covering group Sl(2,C), Lie-algebra as tangential space, Lie algebras of orthogonal and unitary groups, representations of finite groups, lemmata of Schur, characters and character tables, representations of SU(2) and sl(2,C), representations of SU(3) and sl(3,C), weight diagrams, roots, Casimir operators, decomposition of tensor products, representations of proper Lorentz group, spinors

Learning Outcome

The student learns about the most important notions and theorems in group theory.

The student learns what  a Lie grroup is and knows several examples in form of the orthogonal and unitary groups.

The student learns that the 3-dimensional rotation group is not simply connected and what consequences this implies for physics.

The student learns how to construct the inequivalent, irreducible representations of a finite group

The student learns that representations of SU(2) and SU(3) are described uniquely  by one- and two-dimensional weight diagrams, respectively and how their properties can be deduced from these diagrams.


Linear algebra,  basic quantum mechanics

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Group Theory in Physics Kaiser, N. Freitag, 14:00–17:00
sowie einzelne oder verschobene Termine

Learning and Teaching Methods

Oral presentation with writing on black board supplemented by transparencies


Oral presentation with writing on black board supplemented by transparencies



Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.