1. komponenta

Lecture type	Total
Lectures	15
Exercises	15

* Load is given in academic hour (1 academic hour = 45 minutes)

Basics of group theory and their representations. Representations of finite groups with particular attention to symmetric groups. Finite-dimensional representations of classical groups. Young diagrams. Basics of Lie algebras and their representations. Structure of semisimple Lie algebras. Dynkin diagrams. Representations of semisimple Lie algebras. Topological properties of groups and their representations. Connectivity properties of groups. Fundamental group. Basics of theory of Lie groups. The relation between Lie groups and Lie algebras. The course is divided into 15 thematic parts. Every part is covered by 2 hours of lectures.
Thematic parts are the following: I SU(N) groups and algebras; II Killing form; III The structure of simple Lie algebras; IV Simple roots; V Cartan matrix; VI Classical Lie algebras; VII Exceptional Lie algebras; VIII Representations of Lie algebras; IX Casimir operators and the Freudenthal formula; X Weyl group; XI Weyl dimension formula; XII Decomposition of the tensor product of representations; XIII Subalgebras of Lie algebras; XIV Branching rules; XV Elements of supersymmetry and superalgebras.

1. Robert N. Cahn, Semi-Simple Lie Algebras and Their Representations, The Benjamin/Cummings Publ. Co., 1984.
2. A.P. Balachandran et. al. , Group Theory and Hopf Algebra: Lectures for Physicists, World Scientific, 2010.
3. R. Gilmore, Lie groups, Lie algebras and some of their applications, Dover, 2006
4. P. Ramond, Group theory: A Physicist's Survey, Cambridge, 2010
5. Wu-Ki Tung, Group theory in physics, World Scientific, 1985
6. G. Costa, G.Fogli, "Symmetries and Group Theory in Particle Physics", Springer-Verlag, Berlin, 2012.
7. E. Meinrenken: Clifford algebras and Lie theory, Springer, 2013

Fizika elementarnih čestica - Izborni predmeti - Mandatory smjer - Elementary particle physics