The Koslowski–Sahlmann representation: gauge and diffeomorphism invariance
The Koslowski–Sahlmann representation: gauge and diffeomorphism invariance
复制标题
DOI：
10.1088/0264-9381/31/7/075002
复制
发表时间：
2013-11
影响因子：
3.5
通讯作者：
Miguel Campiglia;M. Varadarajan
中科院分区：
文献类型：
--
作者：
Miguel Campiglia;M. Varadarajan
圈量子引力（LQG）的离散空间几何几乎处处是简并的。这与空间无穷大附近的渐近平坦度量的非退化性明显不一致。Koslowski推广了LQG表示，使其能描述光滑非简并三重场标记的态。他的代表性进一步研究了萨尔曼，以期施加规范和空间的非同态不变性，通过组平均方法。出于对渐近平坦量子几何模型的期望，三重标签的状态是非退化在无穷远，但不一定是在内部，我们开始推广Sahlmann的考虑，以三重不同的简并。在这样做的时候，我们包括微妙的相位贡献的平均程序，这是至关重要的正确实施的规范和规范约束，其存在可以追溯到背景指数函数最近由我们之一。我们的处理强调了量子态的对称性在平均过程中的作用。半解析性在LQG美丽的唯一性结果的证明中起着关键作用。作为副产品，我们重新推导出标准LQG的组平均映射，突出了状态对称性的作用，并明确展示其规范的本质独特性。
The discrete spatial geometry underlying loop quantum gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalized the LQG representation so as to describe states labeled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalization of Sahlmann’s considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification.