Canonical approach -- Investigation of finite density QCD phase transition.

The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This is why, we can not calculate physical quantities accurately at finite chemical potential. In this study, we try to beat the sign problem using canonical approach of finite density lattice QCD. Although it is known that the canonical approach has several numerical problems, we can reduce them and calculate thermodynamic observables accurately at finite density. In this thesis, we will see how to improve the canonical approach and a result of thermodynamic observables which are related to the QCD phase transition at finite density. Our study focused on baryon number susceptibility. A peak in baryon number susceptibility corresponds to the confinement--deconfinement phase transition. In this study, we do not see the QCD phase transition yet. However, in this thesis, we find that canonical approach can explore the QCD phase diagram beyond mu_B/T = 3 (mu_B is the baryon chemical potential). That means, we have explored the QCD phase structure beyond the validity range of Taylor expansion and reweighting method. With our improvement, canonical approach has obtained the possibility for investigation of thermodynamic observables at any chemical potential.