Nonconformal scalar field in a homogeneous isotropic space and the Hamiltonian diagonalization method

We diagonalize the metric Hamiltonian and evaluate the energy spectrum of t he corresponding quasiparticles for a scaler field coupled to a curvature i n the case of an N-dimensional homogeneous isotropic space. The energy spec trum for the quasiparticles corresponding to the diagonal form of the canon ical Hamiltonian is also evaluated. We construct a modified energy-momentum tenser with the following properties: for the conformal scaler field, it c oincides with the metric energy-momentum tenser; tile energies of the parti cles corresponding to its diagonal form are equal to the oscillator frequen cy; and the number of such particles created in a nonstationary metric is f inite. We show that the Hamiltonian defined by, the modified energy-momentu m tenser can be obtained as the canonical Hamiltonian under a certain choic e of variables.