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

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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.