  An ordinary unambiguous integral representation for the finite propagator of
a quantum system is found by starting of a privileged skeletonization of the
functional action in phase space, provided by the complete solution of the
Hamilton-Jacobi equation. This representation allows to regard the propagator
as the sum of the contributions coming from paths where the momenta generated
by the complete solution of the Hamilton-Jacobi equation are conserved -as it
does happen on the classical trajectory-, but are not restricted to having the
classical values associated with the boundary conditions for the original
coordinates.
