Study on the non-perturbative propesties of QGP based or low-energy effective theries

(1)应用非微扰重整化群方程(流动方程)研究了有限密度下手征跃迁的性质。在配分函数的积分中首次采用了适时正则化方案。对于含有费米子的线性西格玛模型，成功地得到了流动方程的解析公式。由此得到的流动方程的数值积分在有限密度下给出了相当强的一阶相变。(2)在研究重离子碰撞中手征对称性的可能恢复问题时，探索手征恢复是如何在有限核上发生的是至关重要的。真空的变化可以反映在强子的变化上，即QCD真空顶部的集体激发。用来观察强子性质可能变化的相关观察量是强子通道中的谱函数。当系统在临界点附近时，I=J=O通道中会出现较大的涨落。我们用线性西格玛模型计算了有限Rho_B下的sigma通道的谱函数。我们发现，在两个m&lt；pi&gt；阈值附近，谱函数有一个特征增强。这种增强可能已经被混沌小组在pi+pi-off pi核反应的截面上观察到。我们已经提出了几个实验来进一步探索手性恢复已经在真实核中发生的猜想。(3)应用于手性跃迁的临界现象问题，我发展了重整化群(RG)方法的新公式。作为副产品，我已经证明了RG方法可以用来恢复量子系统波函数的微扰级数。

What has been achieved in the last two years may be summarized as follows :(1)A nonperurbative renormalization group equation (flow equation) has been applied to explore the nature of the chiral transition at finite density. The proper-time regularization scheme has been adopted for the first time in the integral of the partition function. An analytical formula of the flow eauation has been successfully obtained for the linear sigma model with fermions incorporated. A numerical integration of the flow equation thus obtained gives a rather strong first order transition at finite density. Physical implications of the result is now being examined.(2)In examining the problem of the possible restoration of the chiral symmetry as) realized in the heavy-ion collisions, it of fundamental importance to explore how the chiral restoration takes place at finite nuclei. A change of the vacuum can be reflected in that of hadrons, i.e., collective excitations on top of the QCD vacuum. The relevant observable to see the possible change of hadron properties is the spectral function in the hadron channel. One can expect a large fluctuation in the I = J = O channel when the system is near the critical point, We have calculated the spectral function in the sigma channel using a linear sigma model at finite rho_B. We have found that there arises a characteristic enhancement in the spectral function near the two m_<pi> threshold. This enhancement may have been already observed by the CHAOS group in the cross section of pi+pi- off pi-nucleus reaction. We have proposed several experiments to further explore the conjecture that the chiral restoration takes place already in real nuclei.(3)With an application to the problem of the critical phenomena of the chiral transition, I have developed a new formulation of the renormalization group (RG) method. As a by-product, I have shown that the RG method can be applied to resumm the perturbative series of the wave functions of quantum systems.