Koslowski-Sahlmann表示中空间同态的generator
The generator of spatial diffeomorphisms in the Koslowski- Sahlmann representation
摘要：
圈量子引力的离散空间几何的表象的推广，以适应光滑空间几何标记的状态，由科斯洛夫斯基发现，并由Sahlmann进一步研究。我们展示了如何从合适的连接和三元组相关算子中构造Koslowski-Sahlmann（KS）表示中的同构约束算子。我们表明，KS表示支持迄今未被注意到的"背景指数"运营商的行动，在对比的holonomy通量运营商，改变光滑的空间几何标签的国家。这些算子被证明是某些连接依赖函数的量子化，并在构造同构约束算子中起着关键作用。
英文摘要：
A generalization of the representation underlying the discrete spatial geometry of Loop Quantum Gravity, to accomodate states labelled by smooth spatial geometries, was discovered by Koslowski and further studied by Sahlmann. We show how to construct the diffeomorphism constraint operator in this Koslowski- Sahlmann (KS) representation from suitable connection and triad dependent operators. We show that the KS representation supports the action of hitherto unnoticed "background exponential" operators which, in contrast to the holonomy- flux operators, change the smooth spatial geometry label of the states. These operators are shown to be quantizations of certain connection dependent functions and play a key role in the construction of the diffeomorphism constraint operator.
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