标题： 量子自旋动力学（QSD）II 显示英文标题

标题： Quantum Spin Dynamics (QSD) II

摘要： 我们在此继续分析前一篇论文中关于四维、洛伦兹、非微扰、连续体中的规范真空量子引力的Wheeler-DeWitt约束算子的分析。 在本文中，我们推导出Wheeler-DeWitt算子的一种非对称版本的完整核以及在其上的物理内积。 然后我们定义Wheeler-DeWitt算子的一个对称版本。 对于欧几里得Wheeler-DeWitt算子以及从欧几里得区域到洛伦兹区域的Wick变换生成元，我们证明了自伴扩张的存在性，并基于此，我们提出了一种证明洛伦兹算子自伴扩张的方法。 最后，我们根据目前的结果评论Wick旋转变换的现状。 显示英文摘要

摘要： We continue here the analysis of the previous paper of the Wheeler-DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canonical vacuum quantum gravity in the continuum. In this paper we derive the complete kernel, as well as a physical inner product on it, for a non-symmetric version of the Wheeler-DeWitt operator. We then define a symmetric version of the Wheeler-DeWitt operator. For the Euclidean Wheeler-DeWitt operator as well as for the generator of the Wick transform from the Euclidean to the Lorentzian regime we prove existence of self-adjoint extensions and based on these we present a method of proof of self-adjoint extensions for the Lorentzian operator. Finally we comment on the status of the Wick rotation transform in the light of the present results.