On the L—S Basis of the Poincaré Group for the Case of Nonzero Rest Mass

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Abstract
The action of the generators of the Poincaré group on the basis functions spanning an irreducible representation [m2, s2] (m > 0) and labeled by the eigenvalues of the energy, orbital angular momentum and spin, and the projections on a fixed axis of the two latter are considered. The explicit canonical representation of the generators (1.1) are used. The formulas are derived first for the zero‐spin case (Sec. 2) and then for the general case (Sec. 3). It is shown that our L—S basis permits a much more compact and systematic derivation of the formulas than the basis involving total angular momentum and helicity, which is considered by Lomont and Moses. The separation of the orbital and spin parts allows us also to display explicitly the role played by the ``canonical'' definition of spin.