The course takes place in the second half of the spring semester 2019 (2.5 - 28.5) on Tuesdays (7.5 - 28.5, room 119) and Thursdays (2.5 - 23.5, room B1) from 14:15 - 16:00.
Course description
The scope of this series of lectures is twofold:
1) Review the classification of finite dimensional complex semi-simple Lie algebras and their representations. This is based on the description of: weights and roots, Cartan-Weyl basis, Cartan Matrix, Dynkin diagrams, Dynkin labels and related topics. Once introduced these concepts, the aim of this part will be to describe the classification theorem of complex semi-simple Lie algebra and describe how the four classical series and the exceptional algebras arise. These are important tool in studying group theory in particle physics that might not be completely familiar to all PhD students.
2) In the second set of Lectures describe generalisations of the finite dimensional complex Lies algebras including (depending on time):
Infinite dimensional Kac-Moody and affine Lie algebras that play an important role in the study of of two-dimensional conformal field theories and integrable systems;
Super-Lie algebras and groups that are of importance in the study of supersymmetric field and string theories and also integrable systems.
Possible references for topics in the lectures:
- H. Georgi, "Lie Algebras in Particle Physics", Benjamin/Cummings, Reading, Mass., 1982, Gericht op toepassingen
voor Elementaire deeltjesfysica.
- Robert N. Cahn, "Semi-Simple Lie Algebras and Their Representations”
- R. Gilmore, "Lie Groups, Lie Algebras and some of their applications", John Wiley and sons, New York 1974.
Klassieke referentie, volledig en duidelijk uitgelegd. Vele illustraties.
- J. F. Cornwell, "Group theory in Physics", Academic Press, 1984, Vol. 1-3
- W. Fulton and J. Harris "Representation Theory, A First Course,” Springer-Verlag New York
- P. Francesco, D. Sénéchal, P. Mathieuet, "Conformal Field Theories, "Springer
- Fuchs, Schweigert "Symmetries, Lie Algebras and Representations," Cambridge University Press
- Fuchs "Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory,” Cambridge University Press
- S. Reffert, “Groups and Algebras for Theoretical Physics Masters,” based on the course in theoretical physics at The University of Bern (Spring Term 2016)
Lecturer
Dr. G. Tartaglino Mazzucchelli
