MAU34407 Lie groups, Lie algebras and physics
| Module Code | MAU34407 |
|---|---|
| Module Title | Lie groups, Lie algebras and physics |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Chaolun Wu |
| Module Prerequisites | MAU34404 Quantum Mechanics II |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1 which will contribute 70% of the final mark.
- Continuous assessment contributes 30% towards the overall mark.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.
Contact Hours
11 weeks of teaching with 3 lectures and 1 tutorial per week.
Module content
- Basic concepts and general structures of Lie groups and Lie algebras
- Linear Lie groups and algebras: orthogonal, unitary, symplectic and exceptional
- Root system, Dynkin Diagram and the Classifcation
- Lie groups and algebraic geometry, coset manifolds
- Lie groups and differential geometry
- Representations, Young tableaux and Young diagrams
- Applications in physics and advanced topics
Recommended Reading
The main reference will be the lecture notes. The following textbooks are recommended as supplemental materials, but not as required:
- Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists by R. Gilmore, Cambridge University Press (2008).
- Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics by D. H. Sattinger and O. L. Weaver, Springer-Verlag (1986).
- Lie Algebras and Applications by F. Iachello, Second Edition, Springer-Verlag (2015).