  We develop a quantum kinetic theory of the chiral condensate and meson
quasi-particle excitations using the O(N) linear sigma model which describe the
chiral phase transition both in and out of equilibrium in a unified way. A mean
field approximation is formulated in the presence of mesonic quasi-particle
excitations which are described by generalized Wigner functions. It is shown
that in equilibrium our kinetic equations reduce to the gap equations which
determine the equilibrium condensate amplitude and the effective masses of the
quasi-particle excitations, while linearization of transport equations, near
such equilibrium, determine the dispersion relations of the collective mesonic
excitations at finite temperatures. Although all mass parameters for the meson
excitations become at finite temperature, apparently violating the Goldstone
theorem, the missing Nambu-Goldstone modes are retrieved in the collective
excitations of the system as three degenerate phonon-like modes in the
symmetry-broken phase. We show that the temperature dependence of the pole
masses of the collective pion excitations has non-analytic kink behavior at the
threshold of the quasi-particle excitations in the presence of explicit
symmetry breaking interaction.
