Heisenberg-picture approach to the evolution of the scalar fields in an expanding universe

We present the Heisenberg-picture approach to the quantum evolution of the scalar fields in an expanding Friedmann-Robertson-Walker 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. [S0556-2821(97)06018-9]. PACS number(s): 04.62.+v.