The Representations of the Inhomogeneous Lorentz Group in Terms of an Angular Momentum Basis

Abstract

The irreducible ray representations of the proper, orthochronous, inhomogeneous Lorentz group were originally given by Wigner in terms of a basis in which the energy and linear momenta are diagonal. In the present paper we show how the infinitesimal generators of the irreducible representations act on a basis in which the energy, the square of the angular momentum, the component of the angular momentum along the z axis, and the helicity (or circular polarization) are diagonal. We consider representations corresponding to particles of nonzero mass, and any spin and of zero mass and finite spin. The continuous-spin case is to be treated in a later paper.