  A kinetic theory of vacuum particle creation under the action of an inertial
mechanism is constructed within a nonpertrubative dynamical approach. At the
semi-phenomenological level, the inertial mechanism corresponds to quantum
field theory with a time-dependent mass. At the microscopic level, such a
dependence may be caused by different reasons: The non-stationary Higgs
mechanism, the influence of a mean field or condensate, the presence of the
conformal multiplier in the scalar-tensor gravitation theory etc. In what
follows, a kinetic theory in the collisionless approximation is developed for
scalar, spinor and massive vector fields in the framework of the oscillator
representation, which is an effective tool for transition to the quasiparticle
description and for derivation of non-Markovian kinetic equations. Properties
of these equations and relevant observables (particle number and energy
densities, pressure) are studied. The developed theory is applied here to
describe the vacuum matter creation in conformal cosmological models and
discuss the problem of the observed number density of photons in the cosmic
microwave background radiation. As other example, the self-consistent evolution
of scalar fields with non-monotonic self-interaction potentials (the
W-potential and Witten - Di Vecchia - Veneziano model) is considered. In
particular, conditions for appearance of tachyonic modes and a problem of the
relevant definition of a vacuum state are considered.
