时空量子涨落的表述与间接证明及分数阶量子引力应用的合理性论证
Formulating and indirectly proving the quantum fluctuations of space-time and a justification for applying fractional quantum gravity
AI总结：
本文为四十多年历史的量子引力理论建立了数学表述，得出分数阶量子引力方程并间接证明了时空量子涨落的存在，同时论证了分数阶引力源于时空的随机量子涨落，为其实际应用提供了根本依据。
摘要：
众所周知，在量子引力中，时空本身的几何结构会经历持续的涨落。这一古老理论的数学表述至今仍然缺失。本文对这一具有四十多年历史的量子引力理论进行了数学表述，其结果是量子引力方程变为分数阶形式，并间接证明了此类涨落的存在。另一方面，近期分数阶引力受到了关注。尽管这种引力给出了出色的结果，但除了其有效之外，我们缺乏应用它的根本依据和逻辑理由。我们实际上同时证明了分数阶引力是由时空的随机量子涨落产生的。为了澄清这一点，在变形和非变形的minisuperspace（微型超空间）中，研究了包含标量场的Einstein-Hilbert理论。结果展示了从减速膨胀到加速膨胀（晚期加速膨胀）的转变。
英文摘要：
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old theory of quantum gravity, the result of which is that the equations of quantum gravity become fractional. The existence of such fluctuations is proved indirectly. On the other hand, recent attention has been paid to fractional gravity. Although this type of gravity leads to brilliant results, we have no root and logical reason for applying it other than that it works. We actually simultaneously demonstrate that fractional gravity is generated by stochastic quantum fluctuations of space-time. For clarification, Einstein-Hilbert theory along with a scalar field is investigated in deformed and non-deformed minisuperspaces. The results illustrate a transition from decelerated to accelerated expansion (late-time-accelerated expansion).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
