Diagonalization of bilinear bose Hamiltonians and asymptotic behavior of the Heisenberg fields they generate

Necessary and sufficient conditions are obtained for bilinear real Bose Hamiltonians to be diagonalizable by means of a canonical Bogolyubov transformation; expressions are given for the coefficients of the diagonal form. In particular, it is shown that semibounded Hamiltonians of the considered class are always diagonalizable. The intimately related question of asymptotic boundedness of the Heisenberg fields corresponding to bilinear Hamiltonians is studied. Conditions are found under which these Hamiltonians generate asymptotically bounded fields.