Effective Descriptions of Quantum Gravity and Cosmology

广义相对论和量子力学是支配基础物理学的两大理论。然而，大多数已知的数学方法都不足以对这些理论的组合进行完整的分析，即量子引力。因此，大爆炸的最初阶段或黑洞的核心等迷人的现象，在我们目前的理解范围内仍然遥不可及。该项目通过推导新方法和研究与广义相对论和量子力学相关的系统来促进科学的进步。应用于大爆炸和黑洞的数学模型将得出公众普遍感兴趣的结论。它们进一步加深了我们对宇宙的认识，例如，它们为强引力场的广义相对论提供了新的检验。本项目中导出的方法也可用于不涉及广义相对论的系统，它们可能有助于解决技术问题或以一种新的方式传达结果。因此，该项目支持教育，例如在量子力学教学中。该项目还支持多样性，包括来自代表性不足群体的本科生和研究生。该项目的目的是介绍和评估新的方法，以系统地分析一组候选量子引力理论的物理含义，基于规范量子化。在整个物理学中，有效的理论提供了一个强大的工具来推导潜在的可观察现象，这些理论为经典方程提供了量子修正。与量子态方程相比，这样的系统可以更容易地进行分析或数值评估。因此，它们是发现新现象的更直接的来源。虽然推导有效方程的标准技术不适用于经典量子引力，但存在一种适用于经典量子理论的通用方案（由PI引入），并在本项目中用于解决量子引力的一些主要问题。在此资助期间，重点将放在理解量子物理中可能的非联想结构的含义，以及黑洞周围的非经典时空效应。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

General relativity and quantum mechanics are the two major theories that govern fundamental physics. However, the majority of known mathematical methods are insufficient for a complete analysis of a combination of these theories, or quantum gravity. Fascinating phenomena such as the very first stages of the big bang or the cores of black holes therefore remain out of reach for our current understanding. This project promotes the progress of science by deriving new methods and investigating systems in which both general relativity and quantum mechanics are relevant. Applications to mathematical models of the big bang and black holes will lead to conclusions that are of interest to the public at large. They further our knowledge about the universe, for instance by providing new tests of general relativity for strong gravitational fields. Methods derived in this project can also be used for systems that do not involve general relativity, where they may help to solve technical questions or to communicate results in a new way. The project therefore supports education, for instance in teaching quantum mechanics. This project also supports diversity by including undergraduate and graduate students from underrepresented groups.The objective of this project is to introduce and evaluate new methods for a systematic analysis of physical implications of one set of candidate theories of quantum gravity, based on canonical quantization. Throughout physics a powerful tool to derive potentially observable phenomena is given by effective theories which provide quantum corrections to the classical equations. Such systems can more easily be evaluated, analytically or numerically, than equations for quantum states. They are therefore more direct sources for the discovery of new phenomena. While standard techniques to derive effective equations do not apply to canonical quantum gravity, a general scheme applicable to canonical quantum theories exists (introduced by the PI) and is used in this project to address some of the main problems of quantum gravity. During this funding period emphasis will be put on understanding implications of possible non-associative structures in quantum physics, as well as non-classical space-time effects around black holes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.