  We present the Heisenberg-picture approach to the quantum evolution of the
scalar fields in an expanding FRW universe which incorporates relatively simply
the initial quantum conditions such as the vacuum state, the thermal
equilibrium state, and the coherent state. We calculate the Wightman function,
two-point function, and correlation function of a massive scalar field. We find
the quantum evolution of fluctuations of a self-interacting field
perturbatively and discuss the renormalization of field equations.
