  We provide a general method for constructing bosonic Bogoliubov
transformations that diagonalize a general class of quadratic Hamiltonians.
These Hamiltonians describe the pair interaction models. Bogoliubov
transformations are constructed algebraically, and the resulting Hamiltonians
become the second quantizations of explicit one-particle Hamiltonians.
Moreover, an explicit formula for the ground state energies is given. Our
method systematically diagonalizes various models of quantum field theory,
including a model of a harmonic oscillator coupled to a Bose field and the
Pauli-Fierz models in the dipole approximation.
