Irreducible representations of the rotation group in terms of the axis and angle of rotation: II. Orthogonality relations between matrix elements and representations of rotations in the parameter space

Abstract

In a previous paper the irreducible representations of the rotation group were given in terms of a parametrization of the rotation through the axis and angle of rotation. In the present paper we give the orthogonality relations between the matrices of two such irreducible representations. We also show how the infinitesimal generators of the rotation group act in the parameter space and show how finite rotations in the parameter space are to be described. Thus the previous paper and the present one can be used to replace completely the usual theory of irreducible representations in terms of the Euler angles by the far more convenient ones in terms of the angle and axis of rotation.