动力学量子几何（DQG计划）
Dynamical Quantum Geometry (DQG Programme)
摘要：
在这篇简短的笔记（写成一封长信）中，我们描述了从一个自同构变体状态构建的环量子几何基础上的Weyl代数的表示的构造，该变体状态对应于环量子几何的“凝聚”，类似于静态空间几何。我们给出了运动学的GNS表示和规范不变的Hilbert空间表示，并证明了几何算符的期望值取经典值加上量子修正，这类似于量子几何的“定域凝聚”.我们描述了一个尺度相关的渐近映射到一个家庭的尺度相关的格点规范理论，尺度分离的基本几何和低能有效的理论，这是描述为自由度的格点规范理论的建设的想法。如果这个想法可以实现，那么很可能证明这个希尔伯特空间除了引力之外还包含规范耦合的“额外自由度”，这可能不是动态无关的。
英文摘要：
In this brief note (written as a lengthy letter), we describe the construction of a representation for the Weyl-algebra underlying Loop Quantum Geometry constructed from a diffeomorphism variant state, which corresponds to a ''condensate'' of Loop Quantum Geometry, resembling a static spatial geometry. We present the kinematical GNS-representation and the gauge- and diffeomorphism invariant Hilbert space representation and show that the expectation values of the geometric operators take essentialy classical values plus quantum corrections, which is similar to a ''local condensate'' of quantum geometry. We describe the idea for the construction of a scale dependent asymptotic map into a family of scale dependent lattice gauge theories, where scale separates the essential geometry and a low energy effective theory, which is described as degrees of freedom in the lattice gauge theory. If this idea can be implemented then it is likely to turn out that this Hilbert space contains in addition to gravity also gauge coupled ''extra degrees of freedom'', which may not be dynamically irrelevant.
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