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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.

available module versions
WS 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 is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

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 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

Courses and Schedule

TypeSWSTitleLecturer(s)Dates
VO 4 Group Theory in Physics Garbrecht, B. Tue, 10:00–12:00, PH 3343
Fri, 12:00–14:00, PH 3343
UE 2 Exercise to Group Theory in Physics
Responsible/Coordination: Garbrecht, B.
Fri, 14:00–16:00, PH 1121

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.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Exam to Group Theory in Physics
Mon, 2020-02-03 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin vor Mo, 23.03.2020. // Dummy date. Contact examiner for individual appointment. Registration for exam date before Mon, 2020-03-23. till 2020-01-15 (cancelation of registration till 2020-02-02)
Tue, 2020-03-24 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin zwischen Di, 24.03.2020 und Sa, 18.04.2020. // Dummy date. Contact examiner for individual appointment. Registration for exam date between Tue, 2020-03-24 and Sat, 2020-04-18. till 2020-03-23
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