标题： 圈量子引力中的狄拉克量子化实现 显示英文标题

标题： Realization of Dirac quantization in loop quantum gravity

摘要： 研究了引力与非转动尘埃场耦合的系统在经典和量子水平上的性质。 系统的纯量约束可以用尘埃时间表示为真正的物理哈密顿量形式。 在环圈量子引力的框架下，纯量约束被提升为耦合系统的合适希尔伯特空间中的一个良定义算符，从而使得物理哈密顿量成为对称算符。 通过去参数化形式，得到了量子纯量约束解的一般表达式，并可以在解的空间上构造可观测量。 此外，借助该系统，狄拉克量子化程序可以在环圈量子引力中完全实现。 显示英文摘要

摘要： The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to a well-defined operator in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian becomes a symmetric operator. By the deparametrized form, a general expression of the solutions to the quantum scalar constraint is obtained, and the observables on the space of solutions can be constructed. Moreover, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system.