Dynamics and Symmetry in Quantum Gravity

基础物理学面临的一个重要问题是，爱因斯坦的引力理论和量子力学的久经考验的定律是如何一致的——量子引力的问题。这个问题对于理解宇宙的起源——大爆炸至关重要。通过使用环量子宇宙学（LQC），在理解大爆炸方面取得了显著进展。环量子宇宙学是环量子引力（LQG）的简化版本，用于将宇宙作为一个整体进行建模。该奖项旨在弥合LQC和完全LQG之间的差距。这样的桥梁将允许未来LQC与数据的比较，从而告诉我们关于量子引力基本定律的确切细节。弥合这一差距需要回答一些有趣的基本概念问题。本研究的第二部分旨在回答关于环形量子引力的费曼历史和公式的关键问题，其中空间和时间以更统一的方式处理，并使该公式更接近完成。通过使研究生能够参与前沿物理学，并与其他研究小组互动，该奖项将对未来科学家的发展产生广泛而长期的影响。研究结果将通过同行评审出版物和科学讲座向科学界传播，并通过公开讲座和其他方式向公众传播。有了这个奖项，LQG动力学的不同建议的观测和宇宙学结果将被研究。为了实现这一目标，PI将首先找到LQC状态嵌入到微分同态不变的LQG状态中，这些状态满足PI团队最近建立的微分同态不变、均匀性和各向同性的量子准则。这种嵌入，适当地正则化，将使LQG中不同的动力学建议能够转化为LQC，从而使用既定的方法区分它们的观察结果。找到相应的LQC动力学的任务将被这样一个事实所简化，即结果的可能性受到微分同态不变性的严重限制，正如PI的小组最近所证明的那样。PI还计划进一步发展LQG的历史总和方法，即自旋泡沫。在PI先前的工作中，对流行的自旋泡沫的EPRL模型进行了修改，以纠正其半经典极限，从而得到了所谓的适当自旋泡沫模型。从那时起，其他研究小组已经指出，这种改进的模型如何解决一些长期存在的自旋泡沫问题。这些可能性，以及自旋泡沫中的其他问题，将在本奖项中进行研究。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。

An important question facing fundamental physics is how the well-tested laws of Einstein's theory of gravity and quantum mechanics are consistent -- the question of quantum gravity. This question is central for understanding the very origin of our universe, the big bang. Remarkable progress in understanding the big bang has occurred through the use of loop quantum cosmology (LQC), a simplified version of loop quantum gravity (LQG) for modeling the universe as a whole. This award seeks to bridge the gap between LQC and full LQG. Such a bridge would allow future comparisons of LQC with data to tell us exact details about the fundamental laws of quantum gravity. Bridging this gap requires answering a number of interesting fundamental conceptual questions. A second part of this research aims to answer key questions regarding the Feynman sum-over-histories formulation of loop quantum gravity, in which space and time are treated in a more unified way, and to bring this formulation closer to completion. By enabling graduate students to participate in frontier physics, and to interact with other research groups, this award will have a broad and long-term impact on the development of future scientists. The results of the research will be disseminated to the scientific community through peer reviewed publication and scientific lectures, as well as to the general public through public lectures and other means.With this award, the observational, cosmological consequences of different proposals for dynamics in LQG will be studied. To accomplish this, the PI will first find an embedding of LQC states into diffeomorphism invariant LQG states that satisfy the diffeomorphism invariant, quantum criterion for homogeneity and isotropy recently established by the PI's group. This embedding, appropriately regularized, will enable different proposals for dynamics in LQG to be translated into LQC, and thereby to distinguish their observational consequences using established methods. The task of finding the corresponding LQC dynamics will be simplified by the fact that the resulting possibilities are severely restricted by diffeomorphism invariance, as proven recently by the PI's group. The PI also plans to further develop the sum over histories approach to LQG, known as spin-foams. In prior work of the PI, the prevailing EPRL model of spin-foams was modified to correct its semiclassical limit, yielding what is called the proper spin-foam model. Since then, other research groups have indicated how this modified model may solve a number of long-standing issues in spin-foams. These possibilities, as well as other issues in spin-foams, will be investigated with the present award.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.