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# 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.

### 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 2022/3SS 2021WS 2019/20WS 2018/9WS 2017/8WS 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.

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

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.

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