研究了非对易空间上的含时Aharonov-Bohm效应。因为在对易空间中的时间依赖情况下没有净Aharonov-Bohm相移，因此，从零的微小偏离表明新的物理学。基于Seiberg-Witten映射，我们得到了非对易空间中一般情况下的规范不变量和Lorentz协变Aharonov-Bohm相移。我们发现，有两种类型的贡献：动量相关和动量无关的修正。对于动量相关修正，磁相移和电相移之间存在抵消，就像对易空间上的情况一样。然而，有一个不平凡的贡献，在动量无关的修正。这对于非对易空间上的与时间无关和与时间相关的Aharonov-Bohm效应都是正确的。然而，对于含时Aharonov-Bohm效应，在交换和非交换空间上都不存在与时间无关的Aharonov-Bohm效应的压倒性背景。因此，依赖于时间的Aharonov-Bohm可以对空间非对易性敏感。\draftnote{The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter $θ$, and through the surface enclosed by the trajectory of charged particle.}更有趣的是，在磁场$B$的条纹数和平均通量$Φ/N$之间存在反共线关系（N是偏移的条纹数）。这种非平凡关系也可以提供一种检验空间非交换性的方法。对于$BΦ/N\sim 1$，我们对实验灵敏度的估计表明，它可以达到$\rm 10GeV$规模。通过采用更强的磁场强度、更大的磁通量以及更高的相移实验精度可以提高这种灵敏度。
英文摘要：
We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics. Based on the Seiberg-Witten map we obtain the gauge invariant and Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov-Bohm effects on the noncommutative space. However, for the time-dependent Aharonov-Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov-Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov-Bohm can be sensitive to the spatial noncommutativity. \draftnote{The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter $θ$, and through the surface enclosed by the trajectory of charged particle.} More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field $B$ and the averaged flux $Φ/N$ (N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For $BΦ/N\sim 1$, our estimation on the experimental sensitivity shows that it can reach the $\rm 10GeV$ scale. This sensitivity can be enhanced by using stronger magnetic field strength, larger magnetic flux, as well as higher experimental precision on the phase shift.
