  We give the generalization of the method of the space-time description of
particle creation by a gravitational field for a scalar field with nonconformal
coupling to the curvature. The space-time correlation function is obtained for
a created pair of the quasi-particles, corresponding to a diagonal form of the
instantaneous Hamiltonian. The case of an adiabatic change of the metric of
homogeneous isotropic space is analyzed. We show that the created pairs of
quasi-particles in de Sitter space should be interpreted as pairs of virtual
particles.
