论文标题
球形对称重力中仅量子指标
Quantum-only metrics in spherically symmetric gravity
论文作者
论文摘要
爱因斯坦对重力场的作用具有一些构成的特性，在量化之后，它是具有量子构型的罕见原型，具有不具有经典的类似物。假设球形对称性是为了降低有效维度，我们已经对蒙特卡洛进行了对路径积分的模拟，并具有过渡概率$ e^{ - β| s |} $。尽管此选择不允许重现完整的动力学，但它确实使我们找到了具有数量级订单的动作$ | s | \ ll \ hbar $的大型度量配置。这些真空波动是平面度量的强烈变形（$ s = 0 $）。它们在标量曲率$ r $中表现出周期性的两极分化。在模拟中，我们修复了长度比例$ l $，并将其分为$ n $子间值。通过将$ n $提高到$ \ sim 10^6 $来研究连续限制；发现平均平方操作$ \ langle s^2 \ rangle $缩放为$ 1/n^2 $，算法的热化发生在非常低的温度（经典极限）。这与先前针对在渐近安全方案中具有稳定共形因子的理论获得的分析结果达到了定性一致。
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to reduce the effective dimensionality, we have performed a Monte Carlo simulation of the path integral with transition probability $e^{-β|S|}$. Although this choice does not allow to reproduce the full dynamics, it does lead us to find a large ensemble of metric configurations having action $|S|\ll \hbar$ by several magnitude orders. These vacuum fluctuations are strong deformations of the flat space metric (for which $S=0$ exactly). They exhibit a periodic polarization in the scalar curvature $R$. In the simulation we fix a length scale $L$ and divide it into $N$ sub-intervals. The continuum limit is investigated by increasing $N$ up to $\sim 10^6$; the average squared action $\langle S^2 \rangle$ is found to scale as $1/N^2$ and thermalization of the algorithm occurs at a very low temperature (classical limit). This is in qualitative agreement with analytical results previously obtained for theories with stabilized conformal factor in the asymptotic safety scenario.
