Study of microscopic and macroscopic QGP phenomenon

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At very high temperature or density such as the very early second of the universe and neutron stars, the confinement is expected to be broken, and QGP (quark-gluon plasma) state may be realized. Now high energy nuclear collision experiments are actively done to find the QGP.At low density and high temperature we have developed a formula to calculate derivatives of hadron masses etc. with respect to the chemical potential and observed the finite signals. We also studied SU(2) QCD and found the drop of the vector meson for the first time in lattice QCD calculations.In order to understand the phase structure of gauge theories in a non-perturbative manner, we have treated the longitudinal and transverse cornponents of gauge fields carefully with Schwinger-Dyson equation, and analyzed the phase structure in details.We studied also higher dimensional effects on low energy effective electro-weak theory in Randall-Sundrum space-time. We started RHIC experiment to search for QGP. We have observed large anisotropic flow, Jet quenching, the suppression of high transverse pion production and strong rapidity correlation in locally conserved quantities.We have developed a real 3+1 dimension relativistic fluid dynamics code, and together with an event-generator of nuclear reaction which describe the early stage of the collisions, we studied the unisotropic expansion of non-central collision under the realistic initial condition.