The Dynamics of Quantum Gravity

一种处理广义相对论等完全受限理论动力学的新范式将继续在经典和量子层面上得到发展。该范式在于构建离散的理论，以便利益的连续统一体理论作为一个明确定义的极限出现。构造离散理论的具体建议，称为“一致离散化”，有几个吸引人的特点。特别是，离散理论不受约束，因此避免了许多使传统量子引力复杂化的困难概念问题，但仍设法提供了一个明确定义的极限，在这个极限中，人们可以恢复感兴趣的连续统理论。出现了一种类似于格点规范理论的范例，在格点规范理论中，离散理论在一个极限过程中被用来定义感兴趣的连续统理论。这种方法已经成功地应用于时空具有一定空间依赖性(即比齐次宇宙论更复杂)但没有真正自由度的情况，最值得注意的是提供了非奇异环路量子引力黑洞的完整时空的表征。NSF的这个奖项将专注于在日益复杂的情况下应用这一范式。这包括标量场的坍塌形成黑洞和相关模型。文中还提出了与量子引力动力学有关的其他问题，如时间问题和量子力学中的测量问题。这项研究计划还通过培训博士后研究员来帮助创造美国物理学的人力资源，并提供了这里介绍的离散化技术也可能适用于其他科学和工程领域的可能性。

A new paradigm for dealing with the dynamics of totally constrained theories like general relativity will continue to be developed both at a classical and quantum level. The paradigm consists in constructing discrete theories such that the continuum theory of interest arises as a well defined limit. The specific proposal for constructing the discrete theories, called "uniform discretizations" has several attractive features. In particular the discrete theories are free of constraints and therefore avoid many of the hard conceptual problems that complicate traditional quantum gravity, and nevertheless manage to provide a well defined limit in which one recovers the continuum theory of interest. A paradigm emerges that is analogous to that of lattice gauge theory, where discrete theories are used in a limiting procedure to define a continuum theory of interest. This approach has already been applied successfully in some situations where the space-time has some spatial dependence (i.e. more complicated than homogeneous cosmologies) but without genuine degrees of freedom, most notably providing a characterization of the complete space-time of a non-singular loop quantum gravity black hole. This NSF award will focus on applying the paradigm in situations of increasing complexity. This includes the collapse of scalar fields to form black holes and related models. It is also proposed to further other topics related to the dynamics of quantum gravity like the problem of time and the issue of measurement in quantum mechanics. This research program also aids in the creation of human resources in US physics through the training of a postdoctoral researcher and provides the possibility that the discretization techniques introduced here may have applicability in other areas of science and engineering as well.