标题： 翻转的自旋泡沫顶点和环引力 显示英文标题

标题： Flipped spinfoam vertex and loop gravity

摘要： 我们为4d环量子引力引入了一个顶点振幅。 我们通过欧几里得广义相对论的Regge离散化的传统量子化推导出它。 这产生了一个自旋泡沫求和，修正了Barrett-Crane理论的一些困难。 第二类简单性约束是弱施加的，而不是像Barrett-Crane理论中那样强施加。 由于量子代数中的翻转，边界态被证明与SO(3)环量子引力的态相匹配——两者可以被识别为同一物理量的本征态——从而解决了将协变SO(4)自旋泡沫形式主义与规范SO(3)自旋网络形式主义联系起来的问题。 顶点振幅是SO(3)和SO(4)-协变的。 它修正了Barrett-Crane顶点的纠缠子依赖性的平凡性，这是导致其无法产生正确传播子张量结构的原因。 该构造还提供了环量子引力运动学和几何量化的独立推导结果。 显示英文摘要

摘要： We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the Barrett-Crane theory. The second class simplicity constraints are imposed weakly, and not strongly as in Barrett-Crane theory. Thanks to a flip in the quantum algebra, the boundary states turn out to match those of SO(3) loop quantum gravity -- the two can be identified as eigenstates of the same physical quantities -- providing a solution to the problem of connecting the covariant SO(4) spinfoam formalism with the canonical SO(3) spin-network one. The vertex amplitude is SO(3) and SO(4)-covariant. It rectifies the triviality of the intertwiner dependence of the Barrett-Crane vertex, which is responsible for its failure to yield the correct propagator tensorial structure. The construction provides also an independent derivation of the kinematics of loop quantum gravity and of the result that geometry is quantized.