The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is con-sidered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently,in which the fre-quencies are separated in the rest frames as in special relativity.It is shown that only in the rest frame vacuum can the Minkowskian flat limit be reached naturally for any momentum,whereas in the adiabatic vacuum,this limit re-mains undefined in rest frames in which the momentum vanishes.An important role is played by the phases of the fundamental solutions in the rest frame vacuum,which must be regularized to obtain the desired Minkowskian flat limits.This procedure fixes the phases of the scalar mode functions and Dirac spinors,resulting in their definitive expressions derived here.The physical consequence is that,in the rest frame vacuum,the flat limits of the one-particle operators are simply the corresponding operators of special relativity.