Group Theory in Physics 1100-TGF
- https://www.fuw.edu.pl/~aszer/Grupy2025/grupy2025.html (term 2024L)
- https://www.fuw.edu.pl/~aszer/Grupy2026/grupy2026.html (term 2025L)
Programme of lectures:
1. Basic properties of groups
2. Actions of groups on sets.
3. Group homomorphism.
4. Foundations of the representation theory.
5. Lie algebras.
6. Classification of Lie algebras.
7. Matrix Lie groups and related algebras.
8. Representations of Lie algebras and groups.
9. Rotation group SO(3) and the Lorentz group SO(1,3).
10. Application of group theory to elementary particle theory and relativity.
In classes students will practise mathematical tools of group theory and its applications.
Estimated time requirements:
Lectures attendance: 45 hrs
Classes attendance: 45 hrs
Preparation for lectures and classes: 15 hours
Preparation for midterm and classroom tests: 15 hours
Preparation to exam: 30 hours
Total: 150 hours
Course coordinators
Main fields of studies for MISMaP
Type of course
Requirements
Mode
Learning outcomes
After the course a student is expected
- to know basic properties of groups and their representations
- to relate Lie groups to corresponding Lie algebras
- to classify Lie algebras
- to know representations of the rotation group and the Lorentz group
- to present applications of group theory in physics
Assessment criteria
Final mark will depend on results of exam, midterm tests and classroom tests. Regular participation in classes and 50% score from the tests or written exam are required.
Bibliography
Textbooks:
1. A. Trautman, Grupy oraz ich reprezentacje
2. J. F. Cornwell, Group theory in physics
3. M. Hamermesh, Teoria grup w zastosowaniu do zagadnień fizycznych
4. W. Wojtyński, Grupy i algebry Liego
5. A.O. Barut i R. Rączka, Theory of group representations and applications
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: