Proposal of a novel type of vacuum condensates and quark confinement

1.我们成功地从胶子和鬼场构造了一个质量维为2的复合算符，它同时具有BRST和反BRST不变性。我们提出了一种质量维为2的真空凝聚。这种质量维为2的真空凝聚的存在意味着非对角胶子获得了它们的质量。这是第一次产生了一个理论解释的红外阿贝尔优势，这是预期举行的观点，双超导图片的QCD真空，使我们能够解释夸克禁闭。事实上，这种真空凝聚的存在得到了物理解释、胶子和鬼传播子中算符乘积展开、胶子和鬼传播子耦合Schwinger-Dyson方程的紫外渐近解以及格点上数值模拟的支持.为了在Yang-Mills理论中明确地提取磁单极子的自由度，我们对Yang-Mills场变量的非线性变化给出了一种新的观点，称为Cho-Faddeev-Niemi分解。这使得人们能够以规范不变的方式定义磁链。我们指出，Savvidy真空中的Nielsen-Olesen不稳定性可以通过Yang-Mills理论中非对角胶子质量的磁双组态产生的某种色磁凝聚来消除。实际上，通过计算SU（2）Yang-Mills理论中单圈能级的有效势，我们发现了这种新型的磁凝聚.此外，我们还提出了质量维为2的规范不变真空凝聚导致具有结孤子解的Faddeev模型，它可能是Yang-米尔斯理论的低能有效理论。

1. We have succeeded to construct a composite operator of mass dimension two from the gluon and ghost field, which is both BRST and anti-BRST invariant. We have proposed a vacuum condensation of mass dimension two. The existence of such a vacuum condensate of mass dimension two implies that off-diagonal gluons acquire their mass. This has yielded for the first time a theoretical explanation for the infrared Abelian dominance which is expected to hold from the viewpoint of dual superconductor picture of QCD vacuum enabling us to explain quark confinement. In fact, the existence of such a vacuum condensate was supported from a physical interpretation, operator product expansion in the gluon and ghost proopagators, the ultra-violet asymptotic solution of the coupled Schwinger-Dyson equation for the gluon and ghost propagators, and numerical simulations on a lattice.2. To extract degrees of freedom for magnetic monopoles explicitly in Yang-Mills theory, we have given a new viewpoint for the non-linear change of variables for the Yang-Mills field called the Cho-Faddeev-Niemi decomposition. This enables one to define the magnetic monopole in the gauge-invariant way. We have shown how to construct a gauge-invariant mass term for gluons.We have pointed out that the Nielsen-Olesen instability for the Savvidy vacuum is cured by a certain type of color magnetic condensation originating from magnetic monopole configurations which provide the mass for off-diagonal gluons in Yang-Mills theory. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential in one-loop level for the SU(2) Yang-Mills theory.3. Moreover, we have suggested that the gauge-invariant vacuum condensation of mass dimension two leads to the Faddeev model with knot soliton solution, which could be a low-energy effective theory of Yang--Mills theory.