In quantum gravity, summing is refining
In quantum gravity, summing is refining
复制标题
在量子引力中，求和就是精炼
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. Smerlak
中科院分区：
文献类型：
--
作者：
C. Rovelli;M. Smerlak
在微扰QED中，近似是通过求和更多的Feynman图来改进的，而在非微扰QCD中，近似是通过细化晶格来改进的。在这里，我们观察到，在量子引力中，这两个过程很可能是相同的。我们概述了自旋泡沫量子引力的组合结构，定义了连续极限，并表明，在一般条件下，精炼泡沫是相同的求和。的条件承担的spinfoam振幅的圆柱形的一致性和适当的组合因素的存在下，相关的实现的不变性。直觉上，格点是空间的点：这些点本身就是引力场的量子，因此格点离散化也是量子的费曼历史。
In perturbative QED, the approximation is improved by summing more Feynman graphs, while in non-perturbative QCD, by refining the lattice. Here we observe that in quantum gravity, the two procedures may well be the same. We outline the combinatorial structure of spinfoam quantum gravity, define the continuum limit and show that under general conditions, refining foams is the same as summing over them. The conditions bear on the cylindrical consistency of the spinfoam amplitudes and on the presence of appropriate combinatorial factors, related to the implementation of diffeomorphism invariance. Intuitively, the sites of the lattice are points of space: these are themselves quanta of the gravitational field, and thus a lattice discretization is also a Feynman history of quanta.