无自旋无质量粒子的五维量子传输解释
Interpretation of the Five Dimensional Quantum Propagation of a Spinless Massless Particle
摘要：
我们考虑一个具有类空间第五维的五维时空。我们通过路径积分实现了一种量子形式，并假设关于5D无质量粒子传播的所有物理信息都由5D时空中零路径上的统计信息提供。如果5维度规与5维坐标无关，则通过沿5维坐标的叶理化，传播问题可以简化为4维，从而得到4维量子力学的一个公式.如果5维度量与时间无关，我们沿着时间坐标进行分层，得到4维统计力学的一个公式。如果5D度规独立于时间和第五坐标，那么量子力学和统计力学是相同的5D现实的图像。我们还讨论了一个适当的空间维度，克莱因-戈登方程，和一个5D狭义相对论的叶理，完成我们的解释的5D几何。
英文摘要：
We consider a five dimensional (5D) space-time with a space-like fifth dimension. We implement a quantum formalism by path integrals, and postulate that all the physical information on a 5D massless particle propagation is provided by the statistics over null paths in this 5D space-time. If the 5D metric is independent of the fifth coordinate, then the propagation problem can be reduced to four dimensions by foliation along the fifth coordinate, and we obtain a formulation of 4D Quantum Mechanics. If the 5D metric is independent of time, we foliate along the time coordinate, and obtain a formulation of 4D Statistical Mechanics. If the 5D metric is independent of both time and the fifth coordinate, then Quantum and Statistical Mechanics are pictures of the same 5D reality. We also discuss the foliation of a proper space dimension, the Klein-Gordon equation, and a 5D Special Relativity, completing our interpretation of the 5D geometry.
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