标题： 全纯环、谱三元组与量子引力 显示英文标题

标题： Holonomy Loops, Spectral Triples & Quantum Gravity

摘要： 我们回顾通过重新排列环量子引力中心元素获得的半有限谱三元组的动机、构造和物理解释。 该三元组基于一个可数的有向图集合，代数由该集合中的广义Holonomy环组成。 狄拉克型算子类似于全局函数导子算子，Holonomy环代数与狄拉克型算子之间的相互作用再现了广义相对论的量子化泊松括号结构。 最后，我们给出一个启发式论证，说明如何从这个谱三元组构造中出现一个量化哈密顿量的自然候选。 显示英文摘要

摘要： We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator and the interaction between the algebra of holonomy loops and the Dirac type operator reproduces the structure of a quantized Poisson bracket of general relativity. Finally we give a heuristic argument as to how a natural candidate for a quantized Hamiltonian might emerge from this spectral triple construction.