Simple Realizations of the Infinitesimal Generators of the Proper Orthochronous Inhomogeneous Lorentz Group for Mass Zero

Abstract

A realization of the infinitesimal generators for the mass‐zero case of the proper orthochronous inhomogeneous Lorentz group is given explicitly for both continuous and discrete spin cases in terms of a uniform notation. The realization for the discrete spin case is unitarily equivalent to that given by Shirokov. For the sake of completeness the infinitesimal generators for the case of nonzero mass, derived by Foldy, are also given. Hence the present paper contains realizations for all irreducible unitary representations of the inhomogeneous Lorentz group of physical interest. Since the irreducible representations of the two‐dimensional Euclidean group play an important role in the massless case, simple realizations of the irreducible representations of the generators of this group are also given.