Monte-Carlo Study of Quark Confinement in QCD

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(Monte-Carlo simulations)1990 : Abelian projection was performed in the lattice SU(2) QCD. Wilson loops and Creutz ratios show abelian dominance in the maximally abelian gauge.1991 : 1) Gauge-fixing ambiguity is found in the maximally abelian gauge.2) Various quantities are measured in the gauge and the abelian dominance is seen all in the data. Two new order parameters of deconfinement phase transition are found, both of which are constructed from abelian monopole currents. It means that the monopoles are important in the confinement mechanism.3) The monopole currents are studied in the momentum space after Fourier transformation. The data show monopole condensation.4) Preliminary data are obtained in the SU (3) QCD. Abelian quantities show the behavior of the first-order phase transition.(Analytic study of infrared effective QCD)1990 : Solving the classical equations of motion numerically, we found static quark-antiquark potential. It is well approximated by the linear plus Yukawa forms. In SU (3) QCD, the vacuum in the confinement phase is near the border between the first and the second-types dual superconductor.1991 : The analysis is extended to the static baryon case. We got the potential for general configuration of the three quarks. It is approximately determined by the linear length of the strings between the sources.Finite-temperature transition is studied using the Dolan-Jackiw method. We found the second-order transition for SU (2) and the first-order transition for SU (3), which is compatible with the data of the Monte-Carlo simulations.