The Dynamics of Quantum Gravity: Symmetry Reduced Models

我们研究了各种1+1维模型系统中的经典量子引力动力学，包括球对称引力与四维场的耦合以及Callan-Giddings-Harvey-Strominger黑洞。所使用的技术包括最近开发的局部规范固定，环量子引力处理，以及处理我们在过去几年中开发的完全约束理论的动力学的新范式。范式包括构建离散的理论，使得利益的连续统理论作为一个明确的极限而出现。它与晶格规范理论有共同之处，在晶格规范理论中，离散理论被用在一个极限过程中来定义感兴趣的连续统理论。这种方法已经成功地应用于一些时空具有一定空间依赖性的情况（即比同质宇宙论更复杂），但没有真正的自由度，最显著的是提供了非奇异环量子引力黑洞的完整时空的表征。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。这些模型包括像Choptuik在引力坍缩中讨论的复杂现象，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时钟和棒在描述量子力学中的作用，将高性能计算技术应用于环量子宇宙学，并探索环量子引力效应在原始黑洞蒸发中的天体物理学含义。这项研究属于基础物理学，即研究物理定律如何结合在一起的研究领域。在这种情况下，支配大尺度宇宙的万有引力定律和描述微观世界的量子力学定律。有时，通过理解物理定律是如何结合在一起的，可以获得非凡的见解，这些见解会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，该提案的更广泛影响是通过培养博士后研究员来帮助创造美国物理学的人力资源，并且这里介绍的技术也可能适用于其他科学和工程领域。除此之外，还计划为公众举办各种外展活动，不仅有助于传播该提案的结果，还有助于传播在环量子引力子领域工作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.