Integration of the infinitesimal generators of the inhomogeneous Lorentz group and application to the transformation of the wave function

Abstract

We integrate the infinitesimal generators of the proper, orthochronous, inhomogeneous Lorentz group for the nonzero mass case when the infinitesimal generators are given in the Foldy-Shirokov form. We also integrate the infinitesimal generators for the zero mass case when they are given in the Lomont-Moses form. The results are essentially the same as those given by Ritus, but we use a notation which we believe is more convenient for our purposes. The formulas of the present paper will be used to obtain properties of generalized spherical harmonics and to obtain the relativistic quantization of the electromagnetic vector potential in an angular momentum basis in papers which we shall write shortly.