Gruppi di Lie, Algebre di Lie e Spin ​

Group theory is a well-known mathematical tool used by physicists for many topics; there- fore, my thesis work is an attempt to fulfill my curiosity about the math environment and its applications in physics. To define and talk about Matrix Lie Groups in chapter 1 there is a brief introduction to Lie Groups, Lie Algebras, and representation theory. In chapter 2 some results of algebraic topology are introduced which are needed to study the topological properties and relation of Matrix Lie Groups. Chapter 3 focuses on the study of SU (2) and SO(3), SU (2) turns out to be the universal cover of SO(3). The fourth and last chapter discusses the action of SO(3) on L2 (R3 ) and the physic applications in quantum mechanics.