  We elaborate further the functional Schr\"{o}dinger-picture approach to the
quantum field in curved spacetimes using the generalized invariant method and
construct explicitly the Fock space, which we relate with the thermal field
theory. We apply the method to a free massive scalar field in the de Sitter
spacetime, and find the exact quantum states, construct the Fock space, and
evaluate the two-point function and correlation function.
