Representation Theory of Lie Groups

29/04/2011 | Seminar talk in Advanced Quantum Mechanics, Humboldt University of Berlin

Groups are an essential building block in algebraic structures: A set of elements and a binary operation are enough to make us calculate. The theory of groups is used in various settings of physics and mathematics. Lie groups bring a connection to differential geometry and they are of special importance in physics where they describe symmetries. This talk is the first of two subsequent parts to give an overview over the importance of groups in theoretical physics. I will shortly recall some (I) Basic definitions, explain (II) Representation theory which allows us to represent groups by endomorphisms over appropriate vector spaces and finally, I will stress the (III) Relevance of representation theory in the setting of coordinate transformations and transformation symmetries.