Unitary Irreducible Representations of the Lorentz Group

Abstract

The unitary irreducible representations of the inhomogeneous, proper Lorentz group are determined, using a prescription given by Wigner, with special emphasis on the case of zero rest mass. The principal results are: (a) the construction of one-component representations for the case of zero mass and discrete spin; (b) the existence of a Foldy-Wouthuysen transformation for zero mass and spin ½; (c) the construction of "position operators" for zero mass and spins ½, 1; (d) the complete synthesis of the Dirac, Majorana, and Maxwell one-particle theories.