标题： 质量间隙和胶子禁闭 显示英文标题

标题： The mass gap and gluon confinement

摘要： 在我们之前的出版物[1]中已经证明，胶子Shwinger-Dyson方程的一般迭代解可以表示（除其不重要的微扰部分外）为严重（即比$1/q^2$更奇异）红外奇异性整数次幂的洛朗展开式，并伴随着相应的质量间隙幂次。 这里显示了需要进行质量间隙的红外重整化以使理论有限。 这导致了规范不变方式下的胶子禁闭准则。 由于红外重整化，最简单的严重红外奇异性$(q^2)^{-2}$仅能存活下来，乘以质量间隙的平方。 它的意义是负责真实QCD真空的大尺度结构的尺度。 严重红外奇异性由分布理论来正则化。 所有这些使得能够精确且唯一地表述完整的胶子传播子，该传播子可用于从第一原理计算真正非微扰的物理量。 显示英文摘要

摘要： In our previous publication [1] it has been proven that the general iteration solution of the gluon Shwinger-Dyson equation can be represented (up to its unimportant perturbative part) as 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. Here it is shown that the infrared renormalization of the mass gap is needed to render theory finite. This leads to the gluon confinement criterion in the gauge-invariant way. As a result of the infrared renormalization the simplest severe infrared singularity $(q^2)^{-2}$ survives only, multiplied by the mass gap squared. Its meaning is the scale responsible for the large scale structure of the true QCD vacuum. The regularization of severe infrared singularities is provided by the theory of distributions. All of this makes it possible to formulate exactly and uniquely the full gluon propagator, which can be used for the calculation of the truly nonperturbative physical quantities from first principles.