First-Principle Calculation of Hadron System at finite Temperature

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Quarks and gluons have a peculiar feature, i.e., "Confinement". Their dynamics, QCD, predicts the violation of the confinement at high temperature. Such state is called "Quark-Gluon Plasma (QGP)", and was realized at the early stage of the universe. Recently high energy heavy ion experiments have been performed extensively in Europe and USA to search for QGP.In this project, we exchanged researchers between Germany and Japan to discuss the behavior of hadrons at finite temperature, calculational algorithms for finite density systems, and to develop an-isotropic lattice for finite temperature study. We have obtained the following results :1. The relation between the pole masses and two-point functions of imaginary time has been clarified. Then we measured the pole and screening masses by lattice QCD and showed their temperature dependence.2. We have analyzed an-isotropic lattice to get high resolution along the temperature direction. We have extended the study to include improved gauge actions.3. To study the system at the early universe and high energy heavy ion collisions, we need to method to analyze the finite density. Because lattice QCD calculation with finite chemical potential is very hard task, a few trials had been done before. We approach the problem from the response of hadron masses with respect to the chemical potential, and color SU(2) theory.4. On the renormalized trajectory, it is expected that the lattice artifact due to the discretization disappears. We have done the renormalization transformation for SU(3) gauge system non-perturbatively, and found the renormalized trajectory.