The Dynamics of Quantum Gravity: Symmetry Reduced Models

我们研究了在各种1+1维模型系统中正则量子引力的动力学，包括四维球对称引力场和Callan-Giddings-Harvey-Strominger黑洞。其中使用的技术是最近开发的本地规范固定，圈量子引力的治疗，和一个新的范式处理完全约束的理论，我们已经在过去几年中发展的动力学。这种范式在于构建离散的理论，使得利息的连续统理论作为一个明确界定的界限而出现。它与格点规范理论有共同之处，格点规范理论中的离散理论被用在一个极限过程中来定义一个连续统理论。这种方法已经成功地应用于某些情况下，时空有一些空间依赖性（即比均匀宇宙学更复杂），但没有真正的自由度，最值得注意的是提供了一个完整的时空的非奇异圈量子引力黑洞的表征。在这里，我们建议将其扩展到依赖于一个空间坐标的更丰富的模型。这些模型包括复杂的现象，如Choptuik在引力坍缩中讨论的现象，并且在量子水平上可以容纳霍金辐射。我们还将继续研究使用物理钟和杆在描述量子力学中的作用，将高性能计算技术应用于圈量子宇宙学，并探索圈量子引力效应在原始黑洞蒸发中的天体物理意义。这项研究符合基础物理学，该研究领域关注物理定律如何结合在一起。在这种情况下，支配宇宙大尺度的引力定律与描述微观世界的量子力学定律。有时，通过理解物理定律如何结合在一起，可以获得显着的见解，从而导致远远超出任何人想象的实际应用。 除了内在的研究方面，这项建议的更广泛的影响是通过培养博士后研究人员，以及这里介绍的技术可能适用于其他科学和工程领域的可能性，帮助创造美国物理学的人力资源。除此之外，还计划为公众开展各种外联活动，不仅有助于传播这一提案的结果，而且有助于传播整个圈量子引力子领域的物理学家社区的结果。

We study the dynamics of canonical quantum gravity in a variety of 1+1 dimensional model systems including spherically symmetric gravity coupled to fields in four dimensions and the Callan-Giddings-Harvey-Strominger black holes. Among the techniques used are recently developed local gauge fixings, loop quantum gravity treatments, and a new paradigm for dealing with the dynamics of totally constrained theories that we have been developing over the last few years. The paradigm consists in constructing discrete theories such that the continuum theory of interest arises as a well defined limit. It has points in common with 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. We propose here to extend it to richer models with dependence on one spatial coordinate. The models include complex phenomena like the one discussed by Choptuik in gravitational collapse and at the quantum level can accommodate Hawking radiation. We also continue our investigation on the role of using physical clocks and rods in describing quantum mechanics, to apply high performance computing techniques to loop quantum cosmology and to explore astrophysical implications of loop quantum gravity effects in the evaporation of primordial black holes.This research fits within fundamental physics, the area of research that concerns itself with how the laws of physics fit together. In this case the laws of gravity that rule the large scales of the universe with the laws of quantum mechanics that describe the microscopic world. Sometimes by understanding how the laws of physics fit together remarkable insights can be achieved that lead to practical applications far beyond what anyone could have envisioned. Apart from the intrinsic research aspects, broader impacts of this proposal are aiding in the creation of human resources in US physics through the training of a postdoctoral researcher and the possibility that the techniques introduced here may have applicability in other areas of science and engineering as well. In addition to that, various outreach activities for the general public are planned that will help not only disseminate the results of this proposal but those of the community of physicists working on the subfield of loop quantum gravity as a whole.