普列班斯基引力的瞬子表示：XVIII。Kodama态的量子化和拟议的解决方案
Instanton representation of Plebanski gravity: XVIII. Quantization and proposed resolution of the Kodama state
摘要：
本文构造了一个希尔伯特状态空间，解决了普列班斯基引力的瞬子表象中GR的初值约束。这些状态被标记为从CDJ矩阵的本征值构造的两个自由位置函数。这包括GR的物理自由度，其半经典极限对应于彼得罗夫I型、D型和O型时空。在这种表示中的哈密顿约束是一个超几何微分方程的状态，我们已经提供了一个封闭的形式的解决方案。此外，我们已经澄清了这个希尔伯特空间结构中的Kodama状态的作用，这提供了一个解决方案，其正常化的问题提出了各种作者。
英文摘要：
In this paper we have constructed a Hilbert space of states solving the initial value constraints of GR in the instanton representation of Plebanski gravity. The states are labelled by two free functions of position constructed from the eigenvalues of the CDJ matrix. This comprises the physical degrees of freedom of GR with a semiclassical limit corresponding to spacetimes of Petrov Type I, D and O. The Hamiltonian constraint in this representation is a hypergeometric differential equation on the states, for which we have provided a closed form solution. Additionally, we have clarified the role of the Kodama state within this Hilbert space structure, which provides a resolution to the issue of its normalizability raised by various authors.
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