We show that a nontrivial topologies of the spatial section of Minkowski space-time allow for motion of a charged particle under quantum vacuum fluctuations of the electromagnetic field. This is a potentially observable effect of these vacuum fluctuations. We derive mean squared velocity dispersion when the charged particle lies in Minkowski space-time with compact spatial sections in one, two and/or three directions. We concretely examine the details of these stochastic motions when the spatial section is endowed with different globally homogeneous and inhomogeneous topologies. We also show that compactification in just one direction of the spatial section of Minkowski space-time is sufficient to give rise to velocity dispersion components in the compact and noncompact directions. The question as to whether these stochastic motions under vacuum fluctuations can locally be used to unveil global (topological) homogeneity and inhomogeneity is discussed. In globally homogeneous space topologically induced velocity dispersion of a charged particle is the same regardless of the particle's position, whereas in globally inhomogeneous the time-evolution of the velocity depends on the particle's position. Finally, by using the Minkowskian topological limit of globally homogeneous spaces we show that the greater is the value of the compact topological length the longer is the time interval within which the velocity dispersion of a charged particle is negligible. This means that no motion of a charged particle under electromagnetic quantum fluctuations is allowed when Minkowski space-time is endowed with the simply-connected spatial topology. The ultimate ground for such stochastic motion of charged particle under electromagnetic quantum vacuum fluctuations is a nontrivial space topology.

中文翻译：

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带电粒子的电磁真空涨落和拓扑感应运动

我们表明，闵可夫斯基时空的空间截面的非平凡拓扑允许带电粒子在电磁场的量子真空波动下运动。这是这些真空波动的潜在可观察影响。当带电粒子位于 Minkowski 时空，在一个、两个和/或三个方向上具有紧凑的空间截面时，我们推导出均方速度色散。当空间截面被赋予不同的全局同质和非同质拓扑时，我们具体研究了这些随机运动的细节。我们还表明，仅在闵可夫斯基时空的空间截面的一个方向上进行紧致化就足以在紧致和非紧致方向上产生速度色散分量。讨论了真空波动下的这些随机运动是否可以局部用于揭示全局（拓扑）同质性和非同质性的问题。在全局均匀空间中，无论粒子的位置如何，拓扑引起的带电粒子的速度色散都是相同的，而在全局不均匀空间中，速度的时间演化取决于粒子的位置。最后，通过使用全局齐次空间的闵可夫斯基拓扑极限，我们表明紧凑拓扑长度的值越大，带电粒子的速度色散可忽略不计的时间间隔越长。这意味着当闵可夫斯基时空具有简单连接的空间拓扑时，不允许带电粒子在电磁量子涨落下运动。在电磁量子真空涨落下带电粒子的这种随机运动的最终基础是非平凡的空间拓扑。