  We formulate a kinetic theory of self-interacting meson fields with an aim to
describe the freezeout stage of the space-time evolution of matter in
ultrarelativistic nuclear collisions. Kinetic equations are obtained from the
Heisenberg equation of motion for a single component real scalar quantum field
taking the mean field approximation for the non-linear interaction. The mesonic
mean field obeys the classical non-linear Klein-Gordon equation with a
modification due to the coupling to mesonic quasi-particle excitations which
are expressed in terms of the Wigner functions of the quantum fluctuations of
the meson field, namely the statistical average of the bilinear forms of the
meson creation and annihilation operators. In the long wavelength limit, the
equations of motion of the diagonal components of the Wigner functions take a
form of Vlasov equation with a particle source and sink which arises due to the
non-vanishing off-diagonal components of the Wigner function expressing
coherent pair-creation and pair-annihilation process in the presence of
non-uniform condensate. We show that in the static homogeneous system, these
kinetic equations reduce to the well-known gap equation in the Hartree
approximation, and hence they may be considered as a generalization of the
Hartree approximation method to non-equilibrium systems. As an application of
these kinetic equations, we compute the dispersion relations of the collective
mesonic excitations in the system near equilibrium.
