标题： 瞬子和磁单极在外色磁场上 显示英文标题

标题： Instanton and Monopole in External Chromomagnetic Fields

摘要： 我们研究了瞬子和磁单极在外加色磁场所具有的性质。通常情况下，在存在外场的情况下，'t Hooft的类比不再是杨-米尔斯场方程的解。因此，我们在非平凡拓扑扇区中探讨具有最小总杨-米尔斯作用量的稳定瞬子解。为此，我们考虑从't Hooft类比的简单叠加规范场和外色场出发，数值化最小化作用量，关于全局颜色取向、各向异性尺度变换以及局部规范类似变换。这里，为了简化起见，外色场被选为沿某一方向的恒定阿贝尔磁场。然后，由于均匀外场的作用，瞬子解的4维旋转对称性O(4)被减少到两个2维旋转对称性$O(2)\times O(2)$。在固定$t$的空间$\mib{R}^{3}$中，我们发现这种瞬子解有一个四极形变。在存在磁场$\vec{H}$时，沿$\vec{H}$方向出现拉长变形。相反地，在存在电场$\vec{E}$时，沿$\vec{E}$方向出现扁平变形。我们进一步讨论了在外场中的最大阿贝尔规范下，瞬子与磁单极之间的局部关联。外场影响着磁单极轨迹在瞬子周围的出现。实际上，在瞬子中心附近出现了一对磁单极和反磁单极，并且这个磁单极环似乎部分屏蔽了外场。 显示英文摘要

摘要： We study properties of instanton and monopole in an external chromomagnetic field. Generally, the 't Hooft ansatz is no longer a solution of the Yang-Mills field equation in the presence of external fields. Therefore, we investigate a stabilized instanton solution with minimal total Yang-Mills action in a nontrivial topological sector. With this aim, we consider numerical minimization of the action with respect to the global color orientation, the anisotropic scale transformation and the local gauge-like transformation starting from a simple superposed gauge field of the 't Hooft ansatz and the external color field. Here, the external color field is, for simplicity, chosen to be a constant Abelian magnetic field along a certain direction. Then, the 4-dimensional rotational symmetry O(4) of the instanton solution is reduced to two 2-dimensional rotational symmetries $O(2)\times O(2)$ due to the effect of a homogeneous external field. In the space $\mib{R}^{3}$ at fixed $t$, we find a quadrupole deformation of this instanton solution. In the presence of a magnetic field $\vec{H}$, a prolate deformation occurs along the direction of $\vec{H}$. Contrastingly, in the presence of an electric field $\vec{E}$ an oblate deformation occurs along the direction of $\vec{E}$. We further discuss the local correlation between the instanton and the monopole in the external field in the maximally Abelian gauge. The external field affects the appearance of the monopole trajectory around the instanton. In fact, a monopole and anti-monopole pair appears around the instanton center, and this monopole loop seems to partially screen the external field.