  The problem of diagonalization of Hamiltonians of N-dimensional boson systems
by means of time-dependent canonical transformations (CT) is considered, the
case of quadratic Hamiltonians being treated in greater detail. The unitary
generator of time-dependent CT which can transform any Hamiltonian to that of a
system of uncoupled stationary oscillators is constructed. The close
relationship between methods of canonical transformations, time-dependent
integrals of motion and dynamical symmetry is noted.
  The diagonalization and symplectic properties of the uncertainty matrix for
2N canonical observables are studied. It is shown that the normalized
uncertainty matrix is symplectic for the squeezed multimode Glauber coherent
states and for the squeezed Fock states with equal photon numbers in each mode.
The Robertson uncertainty relation for the dispersion matrix of canonical
observables is shown to be minimized in squeezed coherent states only.
