Effective Descriptions of Quantum Gravity and Cosmology

广义相对论和量子力学是支配基础物理的两大理论。然而，大多数已知的数学方法不足以对这些理论或量子引力的组合进行完整的分析。因此，令人着迷的现象，如大爆炸的最初阶段或黑洞的核心，仍然是我们目前所不能理解的。这个项目通过推导广义相对论和量子力学都相关的新方法和研究系统来促进科学的进步。将其应用到大爆炸和黑洞的数学模型中，将会得出公众感兴趣的结论。它们进一步加深了我们对宇宙的了解，例如，通过为强引力场提供新的广义相对论测试。在这个项目中得出的方法也可以用于不涉及广义相对论的系统，在那里它们可能有助于解决技术问题或以一种新的方式交流结果。因此，该项目支持教育，例如在教授量子力学方面。这个项目还通过包括来自代表性不足群体的本科生和研究生来支持多样性。该项目的目标是引入和评估基于正则量子化的系统分析一套候选量子引力理论的物理含义的新方法。在整个物理学中，通过对经典方程进行量子修正的有效理论，提供了一个强大的工具来推导潜在的可观测现象。与量子态方程相比，这样的系统更容易从解析或数值上进行评估。因此，它们是发现新现象的更直接来源。虽然推导有效方程的标准技术不适用于正则量子引力，但存在适用于正则量子理论的一般方案(由PI引入)，并在该项目中用于解决量子重力的一些主要问题。在这一资助期间，重点将放在了解量子物理中可能的非缔合结构的影响，以及黑洞周围的非经典时空效应。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.