Quantized meson fields in and out of equilibrium. I : Kinetics of meson condensate and quasi-particle excitations

摘要

We formulate a kinetic theory of self-interacting meson fields with an aim todescribe the freezeout stage of the space-time evolution of matter inultrarelativistic nuclear collisions. Kinetic equations are obtained from theHeisenberg equation of motion for a single component real scalar quantum fieldtaking the mean field approximation for the non-linear interaction. The mesonicmean field obeys the classical non-linear Klein-Gordon equation with amodification due to the coupling to mesonic quasi-particle excitations whichare expressed in terms of the Wigner functions of the quantum fluctuations ofthe meson field, namely the statistical average of the bilinear forms of themeson creation and annihilation operators. In the long wavelength limit, theequations of motion of the diagonal components of the Wigner functions take aform of Vlasov equation with a particle source and sink which arises due to thenon-vanishing off-diagonal components of the Wigner function expressingcoherent pair-creation and pair-annihilation process in the presence ofnon-uniform condensate. We show that in the static homogeneous system, thesekinetic equations reduce to the well-known gap equation in the Hartreeapproximation, and hence they may be considered as a generalization of theHartree approximation method to non-equilibrium systems. As an application ofthese kinetic equations, we compute the dispersion relations of the collectivemesonic excitations in the system near equilibrium.