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

近两年的主要研究成果如下：（1）应用非微扰重整化群方程（流方程）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当时间的正则化方法。本文成功地导出了含费米子的线性σ模型的流场方程的解析公式。由此得到的流动方程的数值积分给出了一个相当强的一阶过渡在有限密度。这一结果的物理意义正在研究中。(2)In研究重离子碰撞中实现的手征对称性的可能恢复问题，探索手征对称性如何在有限核中发生是至关重要的。真空的变化可以反映在强子的变化中，即，量子色动力学真空上的集体激发观察强子性质可能变化的相关观测量是强子通道中的谱函数。当系统在临界点附近时，I = J = O通道会出现较大的涨落。我们用线性σ模型计算了有限ρ_B时σ通道的谱函数。我们发现在两个m_阈值附近谱函数出现特征增强<pi>。这种增强可能已经被混沌组在π + π- off π-核反应的横截面中观察到。我们已经提出了几个实验，以进一步探讨的猜想，手征恢复已经发生在真实的核。（3）应用于手征跃迁的临界现象问题，提出了一种新的重整化群方法。作为一个副产品，我已经表明，RG方法可以应用于计算量子系统的波函数的微扰级数。

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.