Nonlocal Phases of Local Quantum Mechanical Wavefunctions in Static and Time-Dependent Aharonov-Bohm Experiments
Konstantinos Moulopoulos
备注：
49 pages, 1 figure, presented in Conferences "50 years of the Aharonov-Bohm effect and 25 years of the Berry's phase" (Tel Aviv and Bristol), published in Journ. Phys. A. Compared to the published paper, this version has 17 additional lines after eqn.(14) for maximum clarity, and the Abstract has been slightly modified and reduced from the published 2035 characters to the required 1920 characters
发表信息：
Journal of Physics A: Mathematical and Theoretical, vol. 43 (2010), 354019 (32pp)
我们证明了标准狄拉克相因子不是规范变换方程的唯一解。一般规范函数的完全形式（连接在不同的标量和矢量势集合中运动的系统），除了狄拉克相之外，还包含非局部作用的经典场的项（在时空中）对时间相关的薛定谔方程的局部解：薛定谔图像中波函数的相位受到空间和时间上遥远的磁场和电场的非局部影响，in ways方法that are fully充分explored探索.这些贡献超出了通常的Aharonov-Bohm效应（磁或电）。(i)应用于粒子通过静态磁场或电场的情况，导致观察点处Aharonov-Bohm相位的消除;这些都与半经典水平上的行为有关（对于旧的Werner & Brill实验观察，或它们的“电类似物”--或Batelaan & Tonomura最近的报告），但显示出更普遍的（不仅对窄波包成立，而且对完全离域的量子态也成立）。通过使用这些取消，某些以前未注意到的符号错误的文献中得到纠正。(ii)应用于时间依赖的情况下提供了一个补救的错误结果在文献中（关于狄拉克相位因子的不当使用）并导致包含Aharonov-Bohm部分和场非局部部分的相位：它们的竞争被证明恢复了早期“悖论”中的相对论因果性。（如范坎彭思想实验），而更一般的考虑表明，这里发现的时间非定域性部分地证明了薛定谔图像中量子力学波函数相位的因果传播。这可能为解决时间相关的双缝实验和相关的因果问题开辟了一条直接的途径
英文摘要：
We show that the standard Dirac phase factor is not the only solution of the gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schrödinger equation: the phases of wavefunctions in the Schrödinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in ways that are fully explored. These contributions go beyond the usual Aharonov-Bohm effects (magnetic or electric). (i) Application to cases of particles passing through static magnetic or electric fields leads to cancellations of Aharonov-Bohm phases at the observation point; these are linked to behaviors at the semiclassical level (to the old Werner & Brill experimental observations, or their "electric analogs" - or to recent reports of Batelaan & Tonomura) but are shown to be far more general (true not only for narrow wavepackets but also for completely delocalized quantum states). By using these cancellations, certain previously unnoticed sign-errors in the literature are corrected. (ii) Application to time-dependent situations provides a remedy for erroneous results in the literature (on improper uses of Dirac phase factors) and leads to phases that contain an Aharonov-Bohm part and a field-nonlocal part: their competition is shown to recover Relativistic Causality in earlier "paradoxes" (such as the van Kampen thought-experiment), while a more general consideration indicates that the temporal nonlocalities found here demonstrate in part a causal propagation of phases of quantum mechanical wavefunctions in the Schrödinger picture. This may open a direct way to address time-dependent double-slit experiments and the associated causal issues
The Aharonov-Casher and scalar Aharonov-Bohm topological effects
我们重新审视拓扑和非局部性质的Aharonov-Casher和标量Aharonov-Bohm相位效应。U（1）规范结构的基础被明确展示。阐明了拓扑Aharonov-Casher相和标量Aharonov-Bohm相产生的条件。我们分析了M. Peshkin和H. J. Lipkin（Phys. Rev. Lett. 74，2847（1995）），并表明他们是基于错误的哈密顿量，这导致他们的结论不正确。
Reply to "Comment on "Aharonov-Casher and Scalar Aharonov-Bohm Topological Effects""
在这个答复中，我们认为（一）汉密尔顿，方程。(17)在我们的论文中（Phys. Rev. Lett. 108，070405（2012）），绝对是洛伦兹不变量;（ii）生成拓扑Aharonov-Casher（AC）和标量Aharonov-Bohm（SAB）效应的条件是必要的和物理上有意义的;（iii）在Phys. Rev. Lett. 74，2847（1995）和arXiv：1311.4011不适合描述极化的旋量粒子。
在Aharonov-Bohm效应的初始设定下，由规范不变物理流$(-e)\barψ{\boldsymbol γ} ψ$写入的矢势的规范不变物理纵模对Aharonov-Bohm效应有所需的贡献.而矢势的标量模在规范变换下发生变化，成为非物理模，对Aharonov-Bohm效应没有贡献。在原Aharonov-Bohm设置下，物理纵模使Aharonov-Bohm效应真正发生。在Tonomura { \it et al.}的背景下，在磁体被超导材料屏蔽的情况下，由于迈斯纳效应，不仅磁场而且矢势的纵模都变得很大。这样，不仅磁场，而且物理纵模也不会出现在电子运动的区域。在这样的设置中，只有矢量势的标量模式存在于电子行进的区域中，但该模式对Aharonov-Bohm效应没有贡献。然后，理论上，Aharonov-Bohm效应在Tonomura中不发生{ \it et al.}的设置。在量子理论中，电子被看作是波，纵模引起相位的变化，产生Aharonov-Bohm效应。在经典理论中，电子被看作粒子，唯一存在的纵模给出了角动量的变化。对于粒子来说，没有相的概念，因此不存在Aharonov-Bohm效应。
