Perturbative and Non-Perturbative Analyses of Strong Coupling Field Theories

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Recently, there have been many new and/or precise experiments of hadrons, which consist of quarks and gluons and interact strongly. Based on QCD (Quantum Chromo-Dynamics), which is a strong coupling field theory, our group has pursued the perturbative and non-perturbative studies.QCD is expected to have a rich phase structure by changing the temperature and/or density. Indeed high energy heavy ion collision experiments have been done to find such states, and a new state of matter was found at RHIC. Now it is possible to perform a lattice QCD numerical simulation including pair-creating and annihilation of light quarks in the vacuum, i. e. a calculation to simulate a realistic world, and we performed and studied such QCD simulations. Also many experiments including hadron spin measurements were done, and we can apply QCD at small x regions and diffractive scatterings.In order to understand the mechanism of the confinement of quarks, we calculated the instantaneous part of quark potential, i. e., color Coulomb potential based on Gribov-Zwanziger scenario. The non-confinement system discovered at RHIC is not a free gas of quarks and gluons, but strongly interacting system; it is argued that it is a perfect fluid. To check this possibility based on QCD, we calculate the transport coefficients of gluonic matter. We apply also a new method which is valid in a wide range of Q_T to Drell-Yan reaction of polarized protons, and calculated the cross-sections systematically. We analyzed also quark propagators in the confinement and deconfinement phases, and studied its pole structure.