Monte-Carlo Study of Quark Confinement in QCD

（Monte-Carlo simulation）1990：在晶格SU(2) QCD中进行了Abelian投影。Wilson环和Creutz比在最大阿贝尔规范中表现出阿贝尔优势。1991: 1)在最大阿贝尔规中发现了定规歧义。2)在规范中测量了各种量，并且在数据中都可以看到阿贝尔优势。发现了两个新的非定义相变序参量，它们都是由阿贝尔单极电流构造的。这意味着单极子在约束机制中很重要。3)对单极子电流进行傅里叶变换后的动量空间研究。数据显示单极子凝聚。4)在SU (3) QCD中获得初步数据。阿贝尔量显示了一阶相变的行为。（红外有效QCD的解析研究）1990：数值求解经典运动方程，得到静态夸克-反夸克势。它很好地近似于线性加汤川形式。在SU (3) QCD中，约束相的真空位于第一类和第二类双超导体的边界附近。1991年：将分析推广到静态重子的情况。我们得到了三个夸克的一般构型的势。它近似地由信号源之间的弦的线性长度决定。用Dolan-Jackiw方法研究了有限温度转变。我们发现了SU(2)的二阶跃迁和SU(3)的一阶跃迁，这与蒙特卡罗模拟的数据是一致的。

(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.