Loop Quantum Gravity with Cosmological Constant

爱因斯坦的广义相对论（GR）是描述经典引力场物理的理论。GR理论在理解空间和时间的基本方面取得了巨大的进展。该理论成功地预测了宇宙的演化和各种天体物理现象。然而，众所周知，GR是不完整的。它失去了在极强引力场中进行预测的能力，例如在黑洞内部，或者在大爆炸附近的宇宙早期阶段。物理学中最基本的开放问题之一是如何完成GR以预测极强引力场中的物理。我们正在寻找的完整的引力理论被称为“量子引力”。量子引力理论应该在描述黑洞内部的物理学和帮助我们理解大爆炸附近的早期宇宙中发挥至关重要的作用。最终，量子引力将引导我们对空间和时间有革命性的理解，并推进我们对基础物理和各方面应用的研究。该奖项支持被称为“圈量子引力”（LQG）的候选量子引力理论的发展。该项目包含一个教育计划，作为更广泛影响的一部分，并支持大学和公众两级的物理学教育。LQG是一种具有背景独立性和时空结构非微扰量子化特征的理论。本计画的重点是发展四维宇宙常数的LQG理论，特别是自旋泡沫理论。该项目的主要目标和任务是：（1）通过应用数值方法研究Pachner移动引起的自旋泡沫振幅的行为，理解自旋泡沫中光滑弯曲时空的出现，（2）发展具有宇宙学常数的自旋泡沫模型的几个方面，包括数值计算，类时四面体，边界希尔伯特空间和几何算子，（3）用自旋泡沫理论发展了黑洞和宇宙学的量子理论，并数值研究了自旋泡沫LQG在奇点附近的量子行为;（4）阐明了LQG中的费米子耦合，该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响评审标准。

Einstein's General Relativity (GR) is the theory describing the physics of the classical gravitational field. The theory of GR has made tremendous progress in understanding the fundamental aspects of space and time. The theory has been successful in making predictions for the evolution of the universe and various astrophysical phenomena. However it is well-known that GR is incomplete. It loses its capability of making predictions in an extremely strong gravitational field, e.g. inside a black hole, or at the very early stage of universe near the big bang. One of the most fundamental open questions in physics is how to complete GR in order to predict physics in an extremely strong gravitational field. The complete theory of gravity that we are searching for is called "Quantum Gravity". The theory of Quantum Gravity should play a crucial role in describing the physics inside a black hole and helping us to understand the early universe near the big bang. Eventually Quantum Gravity will lead us to a revolutionary understanding of space and time, and advance our research of fundamental physics and applications in all aspects. This award supports the development of a candidate Quantum Gravity theory known as "Loop Quantum Gravity" (LQG). This project contains an education plan as part of the broader impact and supports education in physics at both levels of the university and the general public.LQG is a theory featured with the background independence and non-perturbative quantization of spacetime structure. This project focuses on developing the theory of LQG with cosmological constant in four dimensions, in particular the spinfoam formulation of theory. The main objectives and tasks of this project are: (1) understanding the emergence of smooth curved spacetimes from spinfoams by applying numerical methods to investigate the behavior of spinfoam amplitudes by Pachner moves, (2) developing several aspects of the spinfoam model with cosmological constant, including numerical computations, timelike tetrahedra, the boundary Hilbert space, and geometrical operators, (3) developing the quantum theory of black holes and cosmology with the spinfoam formalism, and investigating numerically the quantum behavior near the singularities from the spinfoam LQG, and (4) clarifying the fermion coupling in LQG, and developing the theory of matter coupling in LQG.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.