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如何在普朗克尺度上保持一致——量子引力问题。这个问题对于理解宇宙的起源，即大爆炸，至关重要。在理解大爆炸方面的大多数显著进展都发生在量子宇宙学的背景下：高度对称的量子模型，因此高度简化，宇宙。虽然这些模型的结构是由完整的量子引力理论指导的，但它们并不是直接从量子引力理论中推导出来的。本奖项旨在缩小这一差距。这将巩固人们对量子宇宙学预测的信心，并允许其见解用于指导量子引力本身的未来发展。本研究的第二部分旨在进一步理解相对较好理解的量子引力标准公式与费曼历史和公式之间的关系，费曼历史和公式以更统一的方式处理空间和时间。通过允许研究生参与前沿物理学，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。

An important question facing fundamental physics is how the well-tested laws of Einstein's theory of gravity and quantum mechanics become consistent at the Planck scale -- the question of quantum gravity. This question is of central importance in understanding the origin of our universe, the big bang. Most of the remarkable progress on understanding the big bang has occurred in the context of quantum cosmology: quantum models of highly symmetric, and therefore highly simplified, universes. While these models have a structure guided by the full theory of quantum gravity, they are not directly derived from it as a quantum theory. The present award seeks to close this gap. This will solidify confidence in the predictions of quantum cosmology and also permit its insights to be used to guide future developments of quantum gravity itself. A second part of this research aims to further understand the relation between the relatively well-understood canonical formulation of quantum gravity and the Feynman sum-over-histories formulation, in which space and time are treated in a more unified way. By allowing 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.