The Rotation Group, Lorentz Group and Lie Groups

This chapter deals mainly, although not entirely, with the rotation group, which is taken as the focus. The groups SO(3) and SU(2) and their representations are discussed in detail because these groups are used ubiquitously in classical and quantum physics. Then Lie groups and Lie algebras are discussed in general. Their connectedness properties are described, which have implications to physics. The Lorentz group SO(3, 1) and its universal covering group SL(2, C) are also discussed. Spinors are introduced in this context. The topological properties of these groups are discussed in the context of compactness and connectedness. Finally, other important related groups that occur in physics are also described briefly.