标题： 杨-米尔斯存在性，质量间隙和胶子禁闭 显示英文标题

标题： Yang-Mills existence, mass gap and gluon confinement

摘要： 证明了如果在$R^4$上存在具有紧致简单规范群的量子杨-米尔斯理论$G=SU(3)$，那么它表现出质量间隙并约束胶子。 在微观的动力学层次上，仅仅基本的四胶子相互作用就使得完整的胶子传播子在红外区域严重奇异，即必须存在一个严格正的质量量纲常数（为简便起见，称为质量间隙）。 胶子的颜色约束是在我们方法中质量间隙的规范不变效应的红外重整化。 所有这些使得能够唯一且精确地确定负责真实QCD基态中非微扰动力学的完整胶子传播子的结构，同时考虑到严重红外奇异性分布的本质。 显示英文摘要

摘要： It is proven that if quantum Yang-Mills with compact simple gauge group $G=SU(3)$ exists on $R^4$, then it exhibits a mass gap and confines gluons. At the microscopic, dynamical level just the fundamental four-gluon interaction makes the full gluon ptopagator severely singular in the infrared, that is, there must be some strictly positive constant of the dimensions of mass (the mass gap, for simplicity). Color confinement of gluons is the infrared renormalization of the mass gap gauge-invariant effect within our approach. All this makes it possible to fix uniqeuly and exactly the structure of the full gluon propagator responsible for the nonperturbative dynamics in the true QCD ground state, taking into account the distribution nature of severe infrared singularities.