Study of quark confinement mechanism using large-scale (parallel) computers

1)在SU (2) QCD中完成了对偶晶格上的块自旋变换。得到的单极子作用是由自作用项和库仑相互作用项组成的简单形式。这种作用可以精确地转化为双金兹堡-朗道模型、类恶棍紧致QED和弦模型。物理弦张力可以很好地再现。2)在SU (3) QCD中也可以导出有效的阿贝尔单极子作用。单极子凝聚现象也会发生。3)利用得到的单极子作用可以构造约束的无序参数。这是第一个准确地从qcd的有效阿贝尔作用中得到的结果。4)用有限尺度方法评估了Polyakov环及其相关器的临界指数。用阿贝尔联结场和单极子贡献表示的Polyakov环给出了三种类型的几乎相同的临界指数。阿贝尔和单极子优势可以定量地表示。5)发现了两个显示阿贝尔和单极子优势的新规。一个是最小化阿贝尔作用，另一个是最小化阿贝尔单极子密度。两者都再现了与最大阿贝尔规范大致相同的物理结果。通用仪表的研究正在进行中。6)从单极子凝聚的角度研究了SU(2)和SU (3) QCD的有限温度相变。完成了全QCD的研究。虽然晶格尺寸太小，夸克质量不够小，但在全QCD中也显示出阿贝尔和单极子优势。这项研究仍在进行中。

1) Block spin transformation on the dual lattice has been done in SU (2) QCD.The monopole action obtained takes a simple form composed of self and Coulomb interaction terms in the long range region. The action can be transformed exactly into those of the dual Ginzburg-Landau model, the Villain-like compact QED and the string model. Physical string tension can be reproduced quite well.2) The effective abelian monopole action can be derived also in SU (3) QCD.Monopole condensation is shown to occur.3) Disorder parameter of confinement can be constructed using the monopole action obtained. This is the first result derived exactly from the effective abelian action of QCD.4) Critical exponents of Polyakov loops and its correlators have been evaluated using finite-size scaling method. Polyakov loops written in terms of abelian link field and also in terms of monopole contribution give almost the same critical exponents of three types. Abelian and monopole dominance can be shown quantitatively.5) Two new gauges showing abelian and monopole dominances have been found. One is to minimize abelian action and the other is to minimize abelian monopole density. Both reproduce about the same physical results as in the maximally abelian gauge. The study in general gauges is in progress.6)Finite-temperature phase transitions of SU (2) and SU (3) QCD have been studied in terms of monopole condensation.7)Study of full QCD has been done. Abelian and monopole dominances are shown to occur also in full QCD,although the lattice size is too small and quark mass is not small enough. The study is still in progress.