In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along a certain direction — the so-called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function [Formula: see text] which rotates the string to another one is a smooth function everywhere in space, except their respective strings. On the strings, [Formula: see text] is a multi-valued function. Consequently, some misunderstandings in the literature are clarified.

中文翻译：

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狄拉克单极子理论中奇异弦旋转的规范变换

在磁单极子和电荷的量子力学相互作用的狄拉克理论中，矢量势从原点沿一定方向到无穷远是奇异的——即所谓的狄拉克弦。施加著名的量化条件，连接到单极子的奇异弦可以通过规范变换任意旋转，因此在物理上是不可观测的。通过推导其解析表达式并分析其性质，我们证明了将字符串旋转到另一个字符串的规范函数[公式：见正文]是空间中除各自字符串之外的任何地方的平滑函数。在字符串上，[Formula: see text] 是一个多值函数。因此，澄清了文献中的一些误解。