标题： 质量间隙与胶子 confinement 显示英文标题

标题： The mass gap and gluon confinement

摘要： 在我们之前发表的文章[1-3]中已经证明，施温格-狄拉克方程对于全胶子传播子的广义迭代解（即当必须对贡献于胶子自能的骨架圈积分进行迭代时，这意味着没有做任何截断/近似）可以代数地（即精确地）分解为两个本质上不同的项之和。 第一项是关于严重（即比$1/q^2$更奇异）红外奇异性整数幂的洛朗展开式，伴随着质量间隙的相应幂次，并且乘以相应的留数。 标准的第二项总是像$1/q^2$一样具有相同的奇异性，而在其他方面则保持不确定。 这里明确表明，只需要对质量间隙进行红外重正化，就可以使理论在胶子部分免受所有严重的红外奇异性影响。 此外，这导致了以规范不变的方式得出胶子禁闭判据。 由于初始洛朗展开式中质量间隙的红外重正化，该展开式经过维数正则化处理后，最简单的严重红外奇异性$(q^2)^{-2}$仍然存在。 它被质量间隙的平方所乘，而后者是负责真实QCD真空中大尺度结构的尺度。 简单严重红外奇异性$\delta$类型的正则化（及其对多圈骨架积分的推广）是由维数正则化方法正确地实现到分布理论中提供的。 这使得能够精确且明确地表述全胶子传播子（除了其不重要的微扰部分）。 显示英文摘要

摘要： In our previous publication [1-3] it has been proven that the general iteration solution of the Shwinger-Dyson equation for the full gluon propagator (i.e., when the skeleton loop integrals, contributing into the gluon self-energy, have to be iterated, which means that no any truncations/approximations have been made) can be algebraically (i.e., exactly) decomposed as the sum of the two principally different terms. The first term is the Laurent expansion in integer powers of severe (i.e., more singular than $1/q^2$) infrared singularities accompanied by the corresponding powers of the mass gap and multiplied by the corresponding residues. The standard second term is always as much singular as $1/q^2$ and otherwise remaining undetermined. Here it is explicitly shown that the infrared renormalization of the mass gap only is needed to render theory free of all severe infrared singularities in the gluon sector. Moreover, this leads to the gluon confinement criterion in a gauge-invariant way. As a result of the infrared renormalization of the mass gap in the initial Laurent expansion, that is dimensionally regularized, the simplest severe infrared singularity $(q^2)^{-2}$ survives only. It is multiplied by the mass gap squared, which is the scale responsible for the large scale structure of the true QCD vacuum. The $\delta$-type regularization of the simplest severe infrared singularity (and its generalization for the multi-loop skeleton integrals) is provided by the dimensional regularization method correctly implemented into the theory of distributions. This makes it possible to formulate exactly and explicitly the full gluon propagator (up to its unimportant perturbative part).