Theoretical Study of the Quark-Gluon Plasma and Ultrarerativistic Nudeus-Nudeus Collisions

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In this research project, we have studied various theoretical problems related to the properties of matter under extreme physical conditions in temperatures and baryon number densities, ranging from the nature of the QCD phase transitions to the signals of the new phase of matter (the quark-gluon plasma) expected to be formed in the course of ultra-relativistic nucleus-nucleus collisions.We have computed the topological susceptibilities in terms of NJL model supplemented with 't Hooft interaction and obtained a results very similar to the lattice QCD results. We also studied the nature of the chiral phase transition and clarified the role of the hydrodynamic mode near the critical end point (CEP) in the QCD phase diagram on temperature v.s. baryon chemical potential plane as well as in the dynamical scaling behavior. The absorption of high energy charmonium traversing in random color medium was studied in order to access the utility of charmonium as a probe of the quark-gluon plasma and we have shown that the high-energy behavior is qualitatively different from the naive nuclear absorption model.In addition to these problems, we obtained many important results in related theoretical problems such as connection of Casimir effect to finite temperature problem, topological model of baryons, spontaneous symmetry breaking in light-front quantization method and the application of the variational method in quantum field theory to the dynamics of Base-Einstein condensates.