随机引力中的分形时空--从反常扩散和相关层次看
Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
摘要：
我们探讨在随机引力理论中，是否非高斯噪声从高阶关联函数的应力张量的量子物质场时，反向反应的时空可能揭示的线索，多尺度结构。反常扩散可以描述测试粒子在分形时空中的经历。量子物质场的关联层次通过每一关联阶的爱因斯坦-朗之万方程组导出几何对象的关联层次。这种相关层次动力学理论的概念框架，辅助随机过程的特点，可以作为一个管道连接低能量的“自下而上”的方法与“自上而下”的量子引力理论预测分形时空的外观在普朗克尺度。
英文摘要：
We explore in stochastic gravity theory whether non-Gaussian noises from the higher order correlation functions of the stress tensor for quantum matter fields when back-reacting on the spacetime may reveal hints of multi-scale structures. Anomalous diffusion may depict how a test particle experiences in a fractal spacetime. The hierarchy of correlations in quantum matter field induces the hierarchy of correlations in geometric objects via the set of Einstein-Langevin equations for each correlation order. This correlation hierarchy kinetic theory conceptual framework, aided by the characteristics of stochastic processes, may serve as a conduit for connecting the low energy `Bottom-Up' approach with the `Top-Down' theories of quantum gravity which predict the appearance of fractal spacetimes at the Planck scale.
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