论文标题
闭合线中的aharonov-bohm效应
The Aharonov-Bohm effect in a closed flux line
论文作者
论文摘要
使用微型环形磁体可说服aharonov-bohm（AB）效应，但几乎总是使用无限长的螺线管或无限长的通量线来解释它。这样做的主要原因是，考虑到环形构型的正式处理AB效应太麻烦了。但是，如果微型环形磁体是由任意形状和大小的闭合通量线建模的，那么对AB效应的形式处理是精确的，非常简化且完善。在这里，我们提出了一种详细介绍该作用的电磁，拓扑和量子力学方面的治疗方法。我们证明，闭合通量线中的AB相由链接数确定，并且与无限长的通量线中的AB相具有相同的形式，该速度由绕组数确定。我们明确表明，与闭合通量线中的AB效应相关的两缝干扰移位与与无限长的通量线相同。我们通过证明该相在电荷路径的变形下，封闭通量线的变形，电荷路径的同时变形和封闭的通量线以及电荷路径和闭合通量线之间的互换来强调闭合通量线中AB相的拓扑性质。我们还讨论了闭合通量线中AB效应的局部和非局部解释，并引入了一个非单个量规，在所有空间中，矢量的潜在在所有空间中都消失了，除了在被封闭的通量线所包围的表面上消失，这意味着沿着电荷粒子的路径为零，除了该路径在封闭的范围内构成的封闭范围的范围，这是一个封闭的范围，这是一个封闭的范围，这是一个封闭的范围，这是一个问题，这是一个问题，这是一个问题，这是一个问题，结果是，这是一个范围的范围，这是一定的。 AB效应。
The Aharonov-Bohm (AB) effect was convincingly demonstrated using a micro-sized toroidal magnet but it is almost always explained using an infinitely-long solenoid or an infinitely-long flux line. The main reason for this is that the formal treatment of the AB effect considering a toroidal configuration is too cumbersome. But if the micro-sized toroidal magnet is modelled by a closed flux line of arbitrary shape and size then the formal treatment of the AB effect is exact, considerably simplified, and well-justified. Here we present such a treatment that covers in detail the electromagnetic, topological, and quantum-mechanical aspects of this effect. We demonstrate that the AB phase in a closed flux line is determined by a linking number and has the same form as the AB phase in an infinitely-long flux line which is determined by a winding number. We explicitly show that the two-slit interference shift associated with the AB effect in a closed flux line is the same as that associated with an infinitely-long flux line. We emphasise the topological nature of the AB phase in a closed flux line by demonstrating that this phase is invariant under deformations of the charge path, deformations of the closed flux line, simultaneous deformations of the charge path and the closed flux line, and the interchange between the charge path and the closed flux line. We also discuss the local and nonlocal interpretations of the AB effect in a closed flux line and introduce a non-singular gauge in which the vector potential vanishes in all space except on the surface surrounded by the closed flux line, implying that this potential is zero along the path of the charged particle except on the crossing point where this path intersects the surface bounded by the closed flux line, a result that questions the alleged physical significance of the vector potential and the local interpretation of the AB effect.
