  The basic ideas in the theory of quantum mechanics on phase space are
illustrated through an introduction of generalities, which seem to underlie
most if not all such formulations and follow with examples taken primarily from
kinematical particle model descriptions exhibiting either Galileian or
Lorentzian symmetry. The structures of fundamental importance are the relevant
(Lie) groups of symmetries and their homogeneous (and associated) spaces that,
in the situations of interest, also possess Hamiltonian structures. Comments
are made on the relation between the theory outlined and a recent paper by
Carmeli, Cassinelli, Toigo, and Vacchini.
