  We develop a formalism to investigate the behavior of quantum field and
quantum ground state when the field is coupled to perturbation that
periodically oscillates. Working in the Schroedinger picture of quantum field
theory, we confirm that the phenomenon of parametric resonance in the classical
theory implies an instability of quantum vacuum, and correspondingly it gives
rise to catastrophic particle production if the oscillation lasts indefinitely;
the produced number of particles exponentially increases without bound as time
proceeds. The density matrix describing the limiting stage of the quantum state
is determined by a small set of parameters. Moreover, the energy spectrum and
the intensity of produced particles are worked out in greatest detail in the
limit of weak coupling or small amplitude perturbation. In the case of strong
coupling or large amplitude perturbation the leading adiabatic formula is
derived. Application to cosmological fate of weakly interacting spinless fields
(WISF) such as the invisible axion, the Polonyi, and the modular fields is
discussed. Although very little effect is expected on the invisible axion, the
Polonyi type field has a chance that it catastrophically decays at an early
epoch without much production of entropy, provided that an intrinsic coupling
is large enough.
