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

(1)核介质中手性对称性的部分恢复会导致I = J = 0通道（即σ-介子通道）的谱函数软化，而不管手性对称性是线性还是非线性表示；软化可以解释混沌组的实验数据。手性对称的恢复由非线性手性模型中的一个4pi-NN顶点表示，该顶点已在先前的文献计算中得到考虑。(2)除了7r核反应外，（d, ^3He）和（d, t）反应是探索重核部分还原的一个有趣的探针，因为它们可能产生σ-介原子核。(3)为了检验描述失向手性凝聚物（DCC）的有效方程是扩散型还是波动型，我们尝试通过导数展开一致性地推导出随时间变化的金兹堡-朗道方程（TDGL）。我们已经确定了导数展开中由于朗道阻尼所固有的散度，朗道阻尼是微分方程解的摄动级数中常见的长期项。应用所谓的重整化群（RG）方法，我们成功地获得了恢复系数。目前正在研究与TDGL有关的最终进化方程。(4)应用RG方法，我们给出了从微观推导动力学方程和输运方程的统一和通用理论，这些方程包括场论。

(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.