我們在Ashtekar自伴變數表示的量子重力以及其Barberero-Immirzi推廣中，研究及討論內積與真實性條件。在標架(densitized triad)與外賦曲率(extrinsic curvature)表象下，不同基底間的轉換核心(kernel)以及其波函數間的正逆轉換關係也被明確地計算出來。

The inner product and reality conditions for the Ashtekar formulation of quantum gravity using self-dual variables and its Barbero-Immirzi extension are studied and discuessed. The kernels of transformation between different quantum bases and also the precise relations and inversion prescriptions between wave functions in the connection, densitized triad and extrinsic curvature representations are computed explicilty.

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