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中久经考验的定律如何保持一致--量子引力的问题。这个问题对于理解我们宇宙的起源--大爆炸--至关重要。通过使用环形量子宇宙学(LQC)，这是环形量子引力(LQG)的简化版本，将宇宙作为一个整体建模，在理解大爆炸方面取得了显著进展。该奖项旨在弥合LQC和完整LQG之间的差距。这样的桥梁将允许未来将LQC与数据进行比较，以告诉我们有关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。这项研究的第二部分旨在回答有关循环量子引力的费曼历史求和公式的关键问题，在该公式中，空间和时间以更统一的方式处理，并使该公式更接近完成。通过让研究生参与前沿物理，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和长期的影响。研究结果将通过同行评议的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。通过这个奖项，将研究LQG中不同动力学方案的观测和宇宙学后果。要做到这一点，PI将首先找到LQC态到满足微分同胚不变量的LQG态的嵌入，该LQG态满足PI小组最近建立的同质性和各向同性的量子判据。这种嵌入，适当地正规化，将使LQG中关于动力学的不同建议被转化为LQC，从而使用已建立的方法区分它们的观测结果。找到相应的LQC动力学的任务将被简化，因为所产生的可能性受到微分同态不变性的严格限制，正如最近PI的小组所证明的那样。PI还计划进一步开发LQG的历史总和方法，即所谓的旋转泡沫。在PI之前的工作中，对流行的EPRL自旋泡沫模型进行了修改，以修正其半经典极限，产生了所谓的正确的自旋泡沫模型。从那时起，其他研究小组已经指出，这个修改后的模型可能如何解决旋转泡沫中的一些长期存在的问题。这些可能性以及旋转泡沫中的其他问题将与目前的奖项一起进行调查。该奖项反映了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。

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.