Group Theory in Physics
Module PH2116
Module version of WS 2010/1
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
| available module versions | |||||
|---|---|---|---|---|---|
| WS 2022/3 | SS 2021 | WS 2019/20 | WS 2018/9 | WS 2017/8 | WS 2010/1 |
Basic Information
PH2116 is a semester module in German or English language at Master’s level which is offered irregular.
This module description is valid to SS 2019.
If not stated otherwise for export to a non-physics program the student workload is given in the following table.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 75 h | 5 CP |
Responsible coordinator of the module PH2116 in the version of WS 2010/1 was Norbert Kaiser.
Content, Learning Outcome and Preconditions
Content
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.
Preconditions
Linear algebra, basic quantum mechanics
Courses, Learning and Teaching Methods and Literature
Learning and Teaching Methods
Oral presentation with writing on black board supplemented by transparencies
Media
Oral presentation with writing on black board supplemented by transparencies
Literature
none
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
The exam may be repeated at the end of the semester.