Transformation from a Linear Momentum to an Angular Momentum Basis for Particles of Zero Mass and Finite Spin

Abstract

The infinitesimal generators of the inhomogeneous Lorentz group have been given in a basis in which the components of the linear momentum operators are diagonal and in another basis in which the square of the angular momentum is diagonal for all unitary irreducible ray representations of the group. In the present paper we show how the two bases are related for representations corresponding to zero mass and any (finite) spin. It will be shown how this relation enables one to integrate the infinitesimal generators in the angular momentum basis and thereby permits one to show how the angular momentum of a particle changes under the inhomogeneous Lorentz group. In particular, we study the way that the angular momentum of a massless particle of any spin appears in translated and moving frames of reference.