  A canonical structure compatible with the action of the Lorentz group can be
obtained considering the energy and time as conjugate variables of an extended
phase space. Scalar probability waves, describing free relativistic particles,
are associated with functional coherent states for an extended Liouville
equation. Relativistic action waves are provided by distributions localized in
the momentum space, evolving according to the continuity and Hamilton-Jacobi
equations. Presuming the existence of minimum space and time intervals, the
action distributions take the form of relativistic Wigner functions. The
nonrelativistic quantum dynamics is retrieved approximating the time
distribution function by a Gaussian wave packet.
