  We propose in this paper a quantization scheme for real Klein-Gordon field in
de Sitter spacetime. Our scheme is generally covariant with the help of
vierbein, which is necessary usually for spinor field in curved spacetime. We
first present a Hamiltonian structure, then quantize the field following the
standard approach. For the free field, the time-dependent quantized Hamiltonian
is diagonalized by Bogliubov transformation and the eigen-states at each
instant are interpreted as the observed particle states at that instant. The
interpretation is supported by the known cosmological red-shift formula and the
on-shell condition of 4-momentum for a free field. Though the mathematics is
carried out in term of conformal coordinates for the sake of convenience, the
whole theory can be transformed into any other coordinates based on general
covariance. It is concluded that particle states, such as vacuum states in
particular are time-dependent and vacuum states at one time evolves into
non-vacuum states at later times. Formalism of perturbational is provided with
an extended Dirac picture.
