论文标题
有限间隙和动力学质量的量子重力
Quantum gravity on finite spacetimes and dynamical mass
论文作者
论文摘要
我们使用“量子Riemannian几何形状”的新形式主义回顾了量子重力模型，以在有限的离散空间和模糊的矩阵代数上构建它。形式主义以“差分结构”开头，作为biModule $ω^1 $的差分1形，上面是坐标代数$ a $，这可能是不合同的。量子公制是$ω^1 \otimes_aΩ^1 $的非交通级别（0,2）张量，然后为其搜索量子Levi-civita连接（这不再是唯一或保证的）。我们概述了迄今为止在这种形式主义中建立的三个模型，其中的共同点以及未来的问题。一种共同点是在强重力极限中，度量期望值的均匀零差异。我们还概述并讨论了使用量子Riemannian几何形状和其他最新结果的量子FLRW宇宙学和黑洞背景的构建。在新的结果中，我们执行了Kaluza-Klein类型分析，在该分析中，我们通过有限的量子riemannian几何形状量量量量，并给出一个示例，其中总空间上的标量场显示为空间上的一个标量字段，并具有动态产生的质量扩散。
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as a bimodule $Ω^1$ of differential 1-forms over the coordinate algebra $A$, which could be noncommutative. A quantum metric is a noncommutative rank (0,2) tensor in $Ω^1\otimes_AΩ^1$, for which we then search for a quantum Levi-Civita connection (this is no longer unique or guaranteed). We outline the three models which have so far been constructed in this formalism, commonalities among them, and issues going forward. One commonality is a uniform nonzero variance of metric expectation values in the strong gravity limit. We also outline and discuss the construction of quantum FLRW cosmology and black-hole backgrounds using quantum Riemannian geometry and other recent results. Among new results, we perform a Kaluza-Klein type analysis where we tensor classical spacetime coordinates with a finite quantum Riemannian geometry and we give an example where a scalar field on the total space appears as a multiplet of scalar fields on spacetime with a spread of dynamically generated masses.
