我們研究四維廣義相對論中的量子約束代數封閉性。在以Ashtekar變數表示的full theory裡，我們驗証特定ordering約束代數封閉性。這對應到Wheeler-DeWitt方程式中某一特定的ordering，不論是以Ashtekar變數或傳統上常用的densitized triad及外賦曲率變數來表示。在此篇論文中將詳盡地探討球對稱量子重力中的變數及量子約束的簡化，並確立其所對應量子約束的約束代數封閉性。

The closure of the quantum constraint algebra of four-dimensional General Relativity is investigated. Closure of the algebra for the full theory with Ashtekar variables for a prescribed ordering is demonstrated. This leads to a specific choice of ordering of operators in the Wheeler-DeWitt equation both with Ashtekar variables and with more conventional densitized triad and extrinsic curvature variables. Reduction of the variables and quantum constraints to spherically symmetric quantum gravity is studied in detail, and closure of the corresponding quantum constraint algebra is also established.

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