  The description of quantum field systems with meta-stable vacuum is motivated
by studies of many physical problems (the decay of disoriented chiral
condensate, the resonant decay of CP-odd meta-stable states, self-consistent
model of QGP pre-equilibrium evolution, the phase transition problem in the
systems with broken symmetry etc). A non-perturbative approach based on the
kinetic description within the framework of the quasi-particle representation
was proposed here. We restrict ourselves to scalar field theory with potentials
of polynomial type. The back reaction mechanism, i.e. the particle production
influence on background field is also discussed. Using the oscillator
representation, we derive the generalized kinetic equation with
non-pertrubative source term for description of particle-antiparticle creation
under action of background field and equation of motion for it. As an
illustrative example we consider one-component scalar theory with double-well
potential. On this example, we study some features of proposed approach, in
particular, the selection problem of stable vacuum state, what allows to avoid
appearance of tachyonic regimes. The similar analysis is possible for some
other models of such kind: the Friedberg-Lee model, the non-linear of $\eta$ --
meson model of Witten--Di Vecchia--Veneziano, end so on.
