论文标题
功能性$ f（r）$近似
The functional $f(R)$ approximation
论文作者
论文摘要
本文是渐近安全性方法中功能性$ f（r）$近似值的评论。它主要集中在使用非自适应截止的公式上，从而产生二阶微分方程。该公式被用作示例，以详细说明如何使用渐近分析和Sturm-Liouville分析来揭示其一些最重要的特性。特别是，如果为所有值适当定义$ - \ infty <r <\ infty $，可以使用这些方法来确定最多有一个离散数量的固定点，这些方法支持有限数量的相关运算符，并且高维操作员的缩放维度是普遍于从单个中近似近似近似值的parametric依赖。还审查了使用自适应截止的配方，并突出显示了主要差异。
This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This formulation is used as an example to give a detailed explanation for how asymptotic analysis and Sturm-Liouville analysis can be used to uncover some of its most important properties. In particular, if defined appropriately for all values $-\infty<R<\infty$, one can use these methods to establish that there are at most a discrete number of fixed points, that these support a finite number of relevant operators, and that the scaling dimension of high dimension operators is universal up to parametric dependence inherited from the single-metric approximation. Formulations using adaptive cutoffs, are also reviewed, and the main differences are highlighted.
