论文标题
仪表独立描述Aharonov-Bohm效应
Gauge independent description of Aharonov-Bohm Effect
论文作者
论文摘要
aharonov-bohm（AB）效应是一种纯量子效应，暗示着带电粒子的波函数的可测量相移，该粒子将位于粒子的区域\ textit {不可访问}中的磁通量包围到粒子中。从经典上讲，这种非本地效应似乎是不可能的，因为洛伦兹的力仅取决于粒子位置的磁场。在量子力学中，哈密顿量，因此schrödinger方程在粒子引起的电流之间具有局部耦合，而电磁矢量电位$ \ mathbf {a} $，它延伸到有限磁场以外的整个空间。这有时被解释为含义，在量子力学中，$ \ mathbf {a} $在某种意义上比$ \ mathbf {b} $更“基本”，尽管前者是依赖性的，因此无法观察到。在这里，我们将在一个一般证明下进行一些例子，证明只要将其作为整个隔离系统的量子动作的一部分，就可以通过仅考虑规格不变的$ \ mathbf {b} $字段来充分考虑AB效应。规格不变的配方的价格是我们必须放弃位置 - 粒子的AB相对于该区域中$ \ Mathbf {B} $ field的动作的变化产生。
The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region \textit{inaccessible} to the particle. Classically, such a non-local effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle. In quantum mechanics, the Hamiltonian, and thus the Schrödinger equation, has a local coupling between the current due to the particle, and the electromagnetic vector potential $\mathbf{A}$, which extends to the entire space beyond the region with finite magnetic field. This has sometimes been interpreted as meaning that in quantum mechanics $\mathbf{A}$ is in some sense more "fundamental" than $\mathbf {B}$ in spite of the former being gauge dependent, and thus unobservable. Here we shall, with a general proof followed by a few examples, demonstrate that the AB-effect can be fully accounted for by considering only the gauge invariant $\mathbf{B}$ field, as long as it is included as part of the quantum action of the entire isolated system. The price for the gauge invariant formulation is that we must give up locality -- the AB-phase for the particle will arise from the change in the action for the $\mathbf{B}$ field in the region inaccessible to the particle.
