论文标题
从时空的量子微观结构的介质尺度上的重力有效作用
Gravitational effective action at mesoscopic scales from the quantum microstructure of spacetime
论文作者
论文摘要
在介观尺度上，重力的量子校正场方程应来自极端，$ω$，与给定几何形状一致的前几何变量的显微镜构型数量。反过来，此$ω$是密度P的所有事件P（$ρ（p）$的产品，与每个事件相关联的显微镜配置。一个人可以预期$ρ\ propto \ sqrt \ sqrt {g} $，因此$ρd^4x $ scales是区域的适当体积。另一方面，按照领先的命令，我们希望超级原则是基于希尔伯特（Hilbert）行动的，这表明$ \lnρ\ propto r $。我展示了这两个显然是矛盾的要求如何通过使用$ \ sqrt {g} $在曲率上，在Riemann正常坐标（RNC）中的功能依赖性以及对Planck尺度上的粗粒。这导致显微镜配置的密度为$ρ=δ^{ - 1} = \ sqrt {g} _ {rnc} $，其中$δ$是粗粒状的van-vleck确定性。该方法还提供了：（a）计算QG校正到场方程的系统方式，以及（b）重力有效作用与时空流体的动力学理论之间的直接联系。
At mesoscopic scales, the quantum corrected field equations of gravity should arise from extremizing, $Ω$, the number of microscopic configurations of pre-geometric variables consistent with a given geometry. This $Ω$, in turn, is the product over all events P of the density, $ρ(P)$, of microscopic configurations associated with each event P. One would have expected $ρ\propto\sqrt{g}$ so that $ρd^4x$ scales as the proper volume of a region. On the other hand, at leading order, we would expect the extremum principle to be based on the Hilbert action, suggesting $\lnρ\propto R$. I show how these two apparently contradictory requirements can be reconciled by using the functional dependence of $\sqrt{g}$ on curvature, in the Riemann normal coordinates (RNC), and coarse-graining over Planck scales. This leads to the density of microscopic configurations to be $ρ= Δ^{-1} = \sqrt{g}_{RNC}$ where $Δ$ is the coarse grained Van-Vleck determinant. The approach also provides: (a) systematic way of computing QG corrections to field equations and (b) a direct link between the effective action for gravity and the kinetic theory of the spacetime fluid.
