Quantum chromodynamics in a finite box

我们研究了有限区间哈密顿系统中的量子色动力学(QCD)，重点研究了它的非微扰特性，如禁闭、手征对称性的动力学破缺和UA(1)反常。规范的固定是通过一系列么正变换来实现的，得到了轴向规范表象中的哈密顿量。有限区间使我们能够研究规范场的零模所起的特殊作用。首先在1 1维的量子电动力学和QCD的情况下阐明了它们的作用，然后类似的考虑导致了对3 1维QCD中的限制的可能的理解.在一个方向上的有限间隔被证明对应于欧几里德路径积分形式中的有限温度的情况，并在此基础上进行了类比研究.与轴向矢量电流的正则化有关的UA(1)反常被研究.规范不变性是关于…的用一个简单的模型研究晶格QCD中的猝灭近似，该模型由自旋系统与简谐振子耦合而成。提出了与绝热近似的相似性，并计划进行进一步的解析和数值分析来证实这种相似性。基于对QCD的洞察，构建了唯象模型，并将其应用于强子能谱和高能反应。核子被描述为基于Nambu-Jona-Lasinio模型的相对论Faddeev方程的束束态解，并计算了其静态性质。结果表明，该模型给出了一个逼真的核子图像。本文还利用核子的相对论夸克模型研究了高能准弹性过程中内部动力学对初态和/或末态相互作用的影响，并考察了色透明的概念。较少

We have studied the quantum chromodynamics (QCD) in the hamiltonian formulation with a finite interval focussing on its non-perturbative features such as confinement, dynamical breakdown of chiral symmetry and UA (1) anomaly.The gauge fixing is carried out by a series of unitary transformations and the hamiltonian in the axial gauge representation is obtained.The finite interval has enabled us to investigate the special role playd by the zero modes of the gauge field. Their role is first clarified in the cases of the quantum electrodynamics and the QCD in 1+1 dimension and then similar considerations lead to the possible understanding of the confinement in the QCD in 3+1 dimension.The finite interval in one direction turns out to correspond to the case of finite temperature in the Eucledean path integral formalism and a study based on this analogy is being carried out.UA (1) anomaly is studied in connection with the regularization of the axial vector current. The gauge invariance is fo … More und not to be sufficient for giving correct anomaly and the further requirements are being examined.The quenched approximation in the lattice QCD is being studied by a simple model consisting of spin systems coupled to harmonic oscillators. A similarity to an adiabatic approximation is suggested and further analytic and numerical analyzes are planned to confirm the similarity.Based on the obtained insights on the QCD,phenomenological models are constructed and applied to hadron spectroscopy and high energy reactions.The nucleon is described as a bound state solution of a relativistic Faddeev equation based on the Nambu-Jona-Lasinio model and its static properties are calculated. The results indicate that the model gives a realistic picture of the nucleion. A relativistic quark model of the nucleon is also used to study the effects of the internal dynamics on the initial and/or final state interactions in high energy quasi-elastic processes and the idea of color transparency is examined. Less