Explicit diagonalization of pair interaction models

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