Aharonov-Bohm相的经典对应物
The classical counterpart of the Aharonov-Bohm phase
摘要：
Aharonov-Bohm相的存在表明磁场在量子力学中可能产生非定域效应。一般认为，磁场的这种非定域行为在经典物理学中是不可能的，这代表了经典力学和量子力学之间的明显区别。与这些信念相反，我们认为，经典对应的Aharonov-Bohm相位，这是确定在这里与电磁角动量的配置所形成的电荷围绕一个无限长的螺线管封闭一个均匀的磁通量，表明磁场可能会产生非局部效应在经典力学。我们详细讨论了这种势头，特别强调其拓扑和非局部功能。动量是拓扑的，因为它取决于电荷在螺线管周围进行的绕组数量，并且是非局部的，因为磁通量在电荷轨迹上的任何点都没有局部后果。拓扑特征允许我们引入累积电磁角动量的概念，非局部特征允许我们谈论可归因于经典电动力学方程的动力学非局部性。
英文摘要：
The existence of the Aharonov-Bohm phase shows that the magnetic field may produce nonlocal effects in quantum mechanics. It is generally believed that such a nonlocal behavior of the magnetic field is not possible in classical physics and that this represents a clear difference between classical and quantum mechanics. Contrary to these beliefs, we argue that the classical counterpart of the Aharonov-Bohm phase, which is identified here with the electromagnetic angular momentum of the configuration formed by an electric charge moving around an infinitely-long solenoid enclosing a uniform magnetic flux, shows that the magnetic field may produce nonlocal effects in classical mechanics. We discuss this momentum in detail by putting special emphasis on its topological and nonlocal features. The momentum is topological because it depends on the number of windings the electric charge carries out around the solenoid and is nonlocal because the magnetic flux has no local consequences at any point on the charge trajectory. The topological feature allows us to introduce the concept of accumulated electromagnetic angular momentum and the nonlocal feature allows us to speak of a dynamical nonlocality attributable to the equations of classical electrodynamics.
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