磁荷和光子质量：物理弦奇点、狄拉克条件和磁约束
Magnetic Charge and Photon Mass: Physical String Singularities, Dirac Condition, and Magnetic Confinement
摘要：
我们找到精确的，简单的解决方案的Proca版本的麦克斯韦方程与磁源。这些解的几个性质与通常的无质量光子磁荷的情况不同：（i）通常的3-矢量势的弦奇点在磁场中变成实奇点;（ii）不同的3-矢量势变成规范不等价和物理上不同的解;（iii）磁场依赖于$r$和$θ$，因此不再是旋转对称的;（iv）即使当电荷和磁荷位于同一位置时，电荷和磁荷的组合系统也携带场角动量（即对于双子）;（v）对于这些双子，尽管光子有质量，但可以恢复标准狄拉克条件。我们讨论这一点的原因。我们的结论是，提出了一个{ \it孤立}磁荷的磁场中的弦奇异性表明磁荷的禁闭机制，类似于QCD中夸克的通量管禁闭。
英文摘要：
We find exact, simple solutions to the Proca version of Maxwell's equations with magnetic sources. Several properties of these solutions differ from the usual case of magnetic charge with a massless photon: (i) the string singularities of the usual 3-vector potentials become real singularities in the magnetic fields; (ii) the different 3-vector potentials become gauge inequivalent and physically distinct solutions; (iii) the magnetic field depends on $r$ and $θ$ and thus is no longer rotationally symmetric; (iv) a combined system of electric and magnetic charge carries a field angular momentum even when the electric and magnetic charges are located at the same place i.e. for dyons); (v) for these dyons one recovers the standard Dirac condition despite the photon being massive. We discuss the reason for this. We conclude by proposing that the string singularity in the magnetic field of an {\it isolated} magnetic charge suggests a confinement mechanism for magnetic charge, similar to the flux tube confinement of quarks in QCD.
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