正则量子引力关系框架中的非超定域性和因果性
Non-Ultralocality and Causality in the Relational Framework of Canonical Quantum Gravity
摘要：
探讨了非超局域约束条件下正则量子引力的关系框架。在证明不存在异常之后，引入了关系框架的空间离散化版本。这使得应用程序的Lieb-Robinson边界上壳单调规范流时，有一个连续的外部“时间”参数。一个显式的Lieb-Robinson界推导出离散狄拉克观测量的交换子的算子范数的微分在壳演化，演示了如何出现一个局部光锥状因果结构。超局部约束不允许通过Lieb-Robinson边界产生这样的结构。光锥的规范和（3 + 1）-diff不变性与量子涨落、非定域性、空间连续极限以及与非对易几何的可能联系等问题一起讨论。
英文摘要：
The relational framework of canonical quantum gravity with non-ultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the application of Lieb-Robinson bounds to on-shell monotonic gauge-flow when there is a continuous external "time" parameter. An explicit Lieb-Robinson bound is derived for the differential on-shell evolution of the operator norm of the commutator of discretized Dirac observables, demonstrating how a local light cone-like causal structure emerges. Ultra-local constraints do not permit such a structure to arise via Lieb-Robinson bounds. Gauge and (3+1)-diff invariance of the light-cone is discussed along with the issues of quantum fluctuations, the nature of the non-localities, the spatial continuum limit, and possible links to non-commutative geometry.
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