论文标题
循环量子重力的宇宙学状态在均匀图上
Cosmological states in loop quantum gravity on homogeneous graphs
论文作者
论文摘要
我们引入了一类状态，其特征是循环量子重力中提出的同质性和各向同性条件，并在钟形态在特殊类别的均质图上给出的构造具体示例。这样的状态提供了宇宙学空间的新表示，可以在循环量子重力的背景下探索宇宙学模型的制定。我们表明，它们的局部几何形状是通过一种节点可观察的与多体量子力学中使用的单体观察物相似的单节点可观察的方式来描述的，并计算代表全球状态对一节点观测值代数的限制的密度矩阵。该密度矩阵的von Neumann熵提供了一个局部区域的纠缠熵的概念，该熵尊重自动形态不变性，并可以应用于涉及不同图形叠加的状态。
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states provide new representations of cosmological spaces that can be explored for the formulation of cosmological models in the context of loop quantum gravity. We show that their local geometry is described in an automorphism-invariant manner by one-node observables analogous to the one-body observables used in many-body quantum mechanics, and compute the density matrix representing the restriction of global states to the algebra of one-node observables. The von Neumann entropy of this density matrix provides a notion of entanglement entropy of a local region which respects automorphism-invariance and can be applied to states involving superpositions of distinct graphs.
