由作为夸克约束器的介子对支撑的磁环
Magnetic monopole loops supported by a meron pair as the quark confiner
摘要：
本文在杨-米尔斯理论中给出规范不变磁单极子的一个定义，而不使用特胡夫特的阿贝尔投影。它们自动从威尔逊圈操作符中出现。这是通过使用非阿贝尔斯托克斯定理重写威尔逊圈算子来证明的。以这种方式定义的磁性物体是余维3的拓扑对象，即，一个四维的循环我们证明了在四维Yang-Mills理论中确实存在这样的磁环。事实上，我们给出了四维欧几里得SU（2）杨-米尔斯理论中连接一对重子的圆形磁单极环的解析解。这是通过求解微分方程的伴随色（磁场）场在两个-meron背景场内最近开发的杨-米尔斯理论的重新表述。我们的解析解对应的数值解发现由Nigelo和Negele的晶格。这一结果有力地表明，正如卡兰、达申和格罗斯很久以前提出的那样，在最初的杨-米尔斯理论中，一个重子对是最相关的夸克限制器。
英文摘要：
We give a definition of gauge-invariant magnetic monopoles in Yang-Mills theory without using the Abelian projection due to 't Hooft. They automatically appear from the Wilson loop operator. This is shown by rewriting the Wilson loop operator using a non-Abelian Stokes theorem. The magnetic monopole defined in this way is a topological object of co-dimension 3, i.e., a loop in four-dimensions. We show that such magnetic loops indeed exist in four-dimensional Yang-Mills theory. In fact, we give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two--meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen and Gross suggested long ago.
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