Geometry of SU(2)

Abstract

In this chapter we describe the geometry of the group SU(2) in detail. We define the canonical coordinates, the generators, the group multiplication, the Casimir operator, and the characters. Further, we compute the left-invariant and the right-invariant vector fields and one-forms and use them to define the bi-invariant metric, the volume form, the connection, the curvature and the geodesic distance. We construct the Laplacian and discuss the heat kernel on the group.