标题： 引力的非规范量子化。 II. 约束条件和物理希尔伯特空间 显示英文标题

标题： Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space

摘要： 通过使用仿射场变量对引力场进行量化的过程继续进行。 为了完整性，首先介绍了选出仿射场的选择标准、约束的替代处理方法以及在施加约束之前场算子的初始超局部表示的选择。 如类似的例子所示，引入和强制执行引力约束将导致算子表示发生足够的变化，以至于初始超局部场算子表示的所有痕迹都会消失。 为了实现这一约束的引入和强制执行，开发并广泛分析了适合正则化的物理希尔伯特空间的再生核的相空间泛函积分表示。 显示英文摘要

摘要： The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and the choice of the initial (before imposition of the constraints) ultralocal representation of the field operators is initially presented. As analogous examples demonstrate, the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical Hilbert space is developed and extensively analyzed.