In this paper, we present a novel semi-classical theory of the electrostatic and magnetostatic fields and explain the nonlocality problem in the context of the Aharonov–Bohm effect [1]. Specifically, we show that the electrostatic and the magnetostatic fields possess a quantum nature that manifests if certain conditions are met. In particular, the wave amplitudes of the fields are seen to exist even in the regions where the classical fields vanish and they operate on the electron wave functions locally as unitary phases. This formulation also sheds light on the quantisation of electric charges and magnetic flux.

中文翻译：

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揭秘 Aharonov-Bohm 效应中的非局域性问题

在本文中，我们提出了一种新的静电场和静磁场半经典理论，并在 Aharonov-Bohm 效应的背景下解释了非定域性问题 [1]。具体来说，我们表明静电场和静磁场具有量子性质，如果满足某些条件就会显现出来。特别是，即使在经典场消失的区域中，也可以看到场的波幅存在，并且它们对电子波函数局部地作为单一相位起作用。该公式还阐明了电荷和磁通量的量子化。