Investigation of the phase structure and excited modes under extremum environment in the strong intaraction

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In the strong interaction governed by the quantum chromodynamics (QCD), it has been shown that the quark-spin polarization is realized at high baryon density by using the Nambu-Jana-Lasinio (NJL) model with the tensor-type four-point interaction between quarks. As the quark-number density is increasing, the spin-polarization occurs. Then, the two-flavor color superconductivity disappears. By using the extended NJL model which incorporates the eight-point interaction between quarks, it has been shown that there exists a new phase in this model in which the chiral symmetry recovers but the elementary excitation on the vacuum corresponds to nucleon. For the pure Yang-Mills gauge theory, the time-dependent variational method has been constructed within the Gaussian functional approximation. The scalar and pseudo scalar glueball masses have been given and the dependence of glueball masses on the QCD running coupling constant and QCD scale parameter has been clarified.