Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Theoretical Physics
- Code
- groupthf17ex
- Title
- Group Theory
- Usual semester
- Autumn
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- en
- Learning outcomes
- Introduce the basic notions of group theory from the perspective of physics applications, a) Knowledge: At the system level and in its context, he/she knows the comprehensive theoretical knowledge of the main topics of physics. He/she knows the theoretical methods of physics, as well as the fields of mathematics related to physics. b) Abilities: Able to recognize the physical principles of natural phenomena, and theoretically interpret these phenomena for scientific purposes. Able to formulate scientific questions related to physics and mathematics. c) Attitude: He/she is constantly striving to expand his/her knowledge and acquire new skills. d) Autonomy and responsibility: In the field of modern physics, he/she has a high degree of independence in elaborating comprehensive and special professional issues, representing and justifying professional views. He/she is aware of the importance of scientific thinking and accurate conception, and he/she formulates his/her opinion taking these into account.
- Course content
- Group axioms. Subgroups and cosets, Normal subgroups and factor groups. Direct products of groups. Group actions. Free groups and presentations. Lie groups: topological properties, Lie algebra, Haar measure. The rotation group. Representation theory: direct sum and tensor product, irreducible decomposition, branching rules. Group characters, orthogonality relations. Projective representations. Polynomial invariants.
- Assessment method
- Oral examination.
- Bibliography
- Alperin-Bell: Groups and representations, Springer.