  On the bosonic Fock space, a family of Bogoliubov transformations
corresponding to a strongly continuous one-parameter group of symplectic maps
R(t) is considered. Under suitable assumptions on the generator A of this
group, which guarantee that the induced representations of CCR are unitarily
equivalent for all time t, it is known that the unitary operator U_{nat}(t)
which implement this transformation gives a prjective unitary representation of
R(t). Under rather general assumptions on the generator A, we prove that the
corresponding Bogoliubov transformations can be implemented by a one-parameter
group U(t) of unitary operators. The generator of U(t) will be called a
Bogoliubov Hamiltonian. We will introduce two kinds of Bogoliubov Hamiltonians
(type I and II) and give conditions so that they are well defined.
