Dynamics and Symmetry in Quantum Gravity

理论物理学中许多最深奥的问题都围绕着爱因斯坦的广义相对论和量子理论的结合，这是20世纪的两大智力成就。由此产生的理论被称为“量子引力”，需要它来更好地理解宇宙的起源、小尺度空间和时间的本质、黑洞内部发生的事情，以及我们宇宙的起源——大爆炸。通过使研究生和博士后参与前沿物理学，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和长期的影响。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。圈量子宇宙学是圈量子引力的简化版本，它将宇宙作为一个整体进行建模，在理解大爆炸方面取得了许多显著进展。这个奖项旨在弥合这个简化模型和全圈量子引力之间的差距，以巩固对前者预测的信心。这涉及到一些有趣的概念性问题，这些问题的主要研究者已经有了初步的答案。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。

Many of the deepest problems in theoretical physics revolve around combining Einstein's theory of general relativity with quantum theory, two of the major intellectual achievements of the twentieth century. The resulting theory is called "quantum gravity" and is needed to better understand the origin of the universe, the nature of space and time on small scales, what happens inside black holes, and the very origin of our universe, the big bang. By enabling graduate students and post-docs 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.Much remarkable progress in understanding the big bang has occurred through the use of loop quantum cosmology, a simplified version of loop quantum gravity which models the universe as a whole. This award seeks to bridge the gap between this simplified model and full loop quantum gravity in order to solidify confidence in the predictions of the former. This involves a number of interesting conceptual questions for which the principal investigator already has preliminary answers. 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.