Chiral transition at high temperature and density and the σ-meson in nuclear medium

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(1) We have shown that partial restoration of chiral symmetry in nuclear medium induces a softening in the spectral function in the I = J = 0 channel, I.e., the σ-meson channel, irrespective of the linear or nonlinear representation of chiral symmetry; the softening can account for the experimental data by CHAOS group. The restoration of chiral symmetry is represented by a 4pi-NN vertex in the nonlinear chiral model that has been taken into account in the previous calculations in the literature.(2) Apart from 7r-nucleus reactions, we have shown (d, ^3He) and (d, t) reactions are interesting as a probe to explore partial restoration in heavy nuclei because they may produce the σ-mesic nuclei.(3) To examine whether the effective equation to describe the disoriented chiral condensate (DCC) is diffusion- or wave-equation type, we tried to deduce the time-dependent Ginzburg-Landau equation (TDGL) consistently by applying the derivative expansion. We have identified the divergence inherent in the derivative expansion due to the Landau damping a secular term familiar in the perturbation series of solutions of differential equations. Applying the so called the renormalization-group (RG) method, we have successfully obtained the resumed coefficients. It is underway to examine the resultant evolution equation has to do with TDGL.(4)Applying the RG method, we have given a unified and general theory for deriving kinetic and transport equations from the microscopic, equations including field theories.