  We describe the quantum dynamics of the Hubbard model at semi-classical
level, by implementing the Time-Dependent Variational Principle (TDVP)
procedure on appropriate macroscopic wavefunctions constructed in terms of
su(2)-coherent states. Within the TDVP procedure, such states turn out to
include a time-dependent quantum phase, part of which can be recognized as
Berry's phase. We derive two new semi-classical model Hamiltonians for
describing the dynamics in the paramagnetic, superconducting, antiferromagnetic
and charge density wave phases and solve the corresponding canonical equations
of motion in various cases. Noticeably, a vortex-like ground state phase
dynamics is found to take place for U>0 away from half filling. Moreover, it
appears that an oscillatory-like ground state dynamics survives at the Fermi
surface at half-filling for any U. The low-energy dynamics is also exactly
solved by separating fast and slow variables. The role of the time-dependent
phase is shown to be particularly interesting in the ordered phases.
