  The real time non-equilibrium evolution of condensates in field theory
requires an initial value problem specifying an initial quantum state or
density matrix. Arbitrary specifications of the initial quantum state (pure or
mixed) results in initial time singularities which are not removed by the usual
renormalization counterterms. We study the initial time singularities in the
linearized equation of motion for the scalar condensate in a renormalizable
Yukawa theory in 3+1 dimensions. In this renormalizable theory the initial time
singularities are enhanced. We present a consistent method for removing these
initial time singularities by specifying initial states where the distribution
of high energy quanta is determined by the initial conditions and the
interaction effects. This is done through a Bogoliubov transformation which is
consistently obtained in a perturbative expansion.The usual renormalization
counterterms and the proper choice of the Bogoliubov coefficients lead to a
singularity free evolution equation. We establish the relationship between the
evolution equations in the linearized approximation and linear response theory.
It is found that only a very specific form of the external source for linear
response leads to a real time evolution equation which is singularity free. We
focus on the evolution of spatially inhomogeneous scalar condensates by
implementing the initial state preparation via a Bogoliubov transformation up
to one-loop. As a concrete application, the evolution equation for an
inhomogenous condensate is solved analytically and the results are carefully
analyzed. Symmetry breaking by initial quantum states is discussed.
