Phenomenology of Chiral Transition at High Temperature and Density

在第一年，我们为Nambu-Jona-Lasinio （NJL）模型开发了一个新的截止方案。该格式基于色散关系，适用于温度(T)和密度（rho）有限的情况。在费曼不等式的基础上，给出了有限温度下的平均场理论的基础。我们计算了在有限T和不同运动条件下介质中的σ介子宽度。在接下来的一年（最后一年），我们提出了几个实验来观察有限密度下介质中西格玛介子的可能质量位移。这是基于标量场和向量场可以在有限密度下混合的观察。我们还提出探测2 ^0来观测sigma介子。我们研究了为什么超导体中的时变现象可以用扩散时变Ginzburug方程来描述，而不是用手性跃迁。这是由于BCS理论所描述的超导体的有效空间维度是1而不是NJL模型中的3。我们还澄清了饱和性质，因此核的稳定性是由于QCD的手性对称性。

In the first year, we developed a new cut-off scheme for the Nambu-Jona-Lasinio (NJL) model. The scheme is based on the dispersion relation and applicable to the finite temperature (T) and density (rho) cases. We also give a foundation to the mean-field theory at finite temperature, on the basis of an inequality due to Feynman. We calculated the width of the sigma meson in the medium at finite T and rho in various kinematical conditions.In the next (final) year, we proposed several experiments to see the possible mass shift of the sigma meson in the medium at finite density. This is based on the observation that scalar and vector fields can mix at finite density. We also proposed to detect 2pi^0 to see the sigma meson.We examined the reason why the time-dependent phenomena in the superconductors may be described in the diffusive time-dependent Ginzburug equation in contrast with the chiral transition. This is due to the fact that the effective spatial dimension of the superconductors as described the BCS theory is one not three as in the NJL model. We also clarified that the saturation properties hence thestability of nuclei is due to chiral symmetry of QCD.