  Canonical variables for the Poisson algebra of quantum moments are introduced
here, expressing semiclassical quantum mechanics as a canonical dynamical
system that extends the classical phase space. New realizations for up to
fourth order in moments for a single classical degree of freedom and to second
order for a pair of classical degrees of freedom are derived and applied to
several model systems. It is shown that these new canonical variables
facilitate the derivation of quantum-statistical quantities and effective
potentials. Moreover, by formulating quantum dynamics in classical language,
these methods result in new heuristic pictures, for instance of tunneling, that
can guide further investigations.
