Representations of the Inhomogeneous Lorentz Group in Terms of an Angular Momentum Basis: Derivation for the Cases of Nonzero Mass and Zero Mass, Discrete Spin

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Abstract
In a previous paper the authors showed how the infinitesimal generators of the proper, orthochronous, inhomogeneous Lorentz group acted in a basis in which the square of the angular momentum, the z component of the angular momentum, the helicity and the energy were diagonal for the irreducible representations which correspond to the cases of nonzero and zero mass, discrete spin. In that paper no derivation of the results were given. It was possible, however, to verify them directly. In the present paper we carry out the derivation.