ON SOME REPRESENTATIONS OF THE POINCARE GROUP ON PHASE-SPACE .2.

Representations of the proper Poincaré group on spaces of functions of the phase space variables q and p have been studied, by starting with the rotation subgroup SO(3), and carrying out an inducing procedure. A complete decomposition theory, for the physically interesting representations, have been developed. Explicit computations of the forms of the generators and certain systems of imprimitivity have been carried out. The role of the Newton-Wigner position and momentum operators, in the setting of phase space representations, has been discussed. The work is a continuation of an earlier paper on phase space representations, inspired ultimately by the possibility of developing a consistent relativistic quantum mechanics for single particles on phase space. © 1980 American Institute of Physics.