标题： 环状自旋网络的福克空间用于量子引力 显示英文标题

标题： The Fock Space of Loopy Spin Networks for Quantum Gravity

摘要： 在环量子引力粗粒化的背景下，我们引入了环状和标记自旋网络，它们将标准自旋网络态推广，以明确考虑非平凡曲率和扭力。 这两种结构放松了在自旋网络顶点处施加的闭合约束。 虽然标记自旋网络仅在每个顶点携带一个额外的自旋，编码整体闭合缺陷，但环状自旋网络允许在每个顶点附加任意数量的环。 这些小环可以被解释为量子引力场的局部激发，并我们讨论了赋予它们统计特性的方法。 环状自旋网络的最终福克空间实现了环量子引力的新截断，使得可以在固定背景图加上与图节点相关的局部自由度上表述其图改变动力学。 这提供了一个框架，重新引入非平凡的背景量子几何，在其周围我们可以研究微扰的有效动力学。 我们研究了如何在这个框架中实现拓扑BF理论的动力学。 我们通过全纯性约束实现了平坦连接的投影，并特别关注由$\delta$分布的高阶导数定义的常被忽视的非平凡平坦解。 显示英文摘要

摘要： In the context of the coarse-graining of loop quantum gravity, we introduce loopy and tagged spin networks, which generalize the standard spin network states to account explicitly for non-trivial curvature and torsion. Both structures relax the closure constraints imposed at the spin network vertices. While tagged spin networks merely carry an extra spin at every vertex encoding the overall closure defect, loopy spin networks allow for an arbitrary number of loops attached to each vertex. These little loops can be interpreted as local excitations of the quantum gravitational field and we discuss the statistics to endow them with. The resulting Fock space of loopy spin networks realizes new truncation of loop quantum gravity, allowing to formulate its graph-changing dynamics on a fixed background graph plus local degrees of freedom attached to the graph nodes. This provides a framework for re-introducing a non-trivial background quantum geometry around which we would study the effective dynamics of perturbations. We study how to implement the dynamics of topological BF theory in this framework. We realize the projection on flat connections through holonomy constraints and we pay special attention to their often overlooked non-trivial flat solutions defined by higher derivatives of the $\delta$-distribution.