International Research Fellowship Program: Moving Forward in Loop Quantum Gravity Via Self-Duality

国际研究奖学金计划：通过自对偶性推进环量子引力

• 批准号: 0601844
• 负责人: Jonathan Engle
• 金额: --
• 依托单位: Engle Jonathan S
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2009-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0601844&HistoricalAwards=false
• 关键词: International; Research; Fellowship; Program; Moving

0601844EngleThe International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support a twenty-four-month research fellowship by Dr. Jonathan S. Engle to work with Dr. Carlo Rovelli at Centre de Physique Theorique, in Marseille, France.Significant progress has been made over the past decade in loop quantum gravity. However, issues remain. One prominent among them is that the implementation of dynamics is conceptually somewhat unnatural and technically quite complex. A direct consequence of this is an inability to fully relate loop quantum gravity to spin-foams, the path integral version of loop quantum gravity. One way of resolving this problem is to use a self-dual formulation of general relativity. Classically, in the self-dual formulation, the dynamics are as simple as they possibly could be. However, in the past, there was an obstacle preventing the rigorous definition of a quantum theory based on the self-dual formulation: One did not know how to construct an acceptable inner-product a notion of "overlap" between states, which is essential in order to extract predictions from the theory. The goal of the project is to find an inner-product for self-dual loop quantum gravity. A number of inner products are available, including gauge and diffeomorphism-invariant ones already mentioned in the literature, as well as a class introduced by the PI. The key question is whether or not any of these implement the correct reality conditions of the self-dual theory --- that is, whether or not any of these are such that complex conjugation at the classical level carries over to Hermitian conjugation at the quantum level. If the PI is successful in finding an acceptable inner product, the PI will try to reproduce quantum geometry in the newly created self-dual framework and then attempt to construct a simplified Hamiltonian constraint. The PI will then see whether the simplified Hamiltonian constraint allows loop quantum gravity to be more directly related to a spin-foam model.

0601844国际研究奖学金计划使美国科学家和工程师能够在国外进行九至二十四个月的研究。 该计划的奖项为联合研究提供了机会，并且在国外使用独特或补充设施，专业知识和实验条件。该奖项将支持Jonathan S. Engle博士与Carlo Rovelli博士在法国Marseille的Theorique Centrique Centrique Theorique Centrique Centrique Centrique Centrique teception to partity partity partity partity partity pardity pardity partity parte decade partity partection。 但是，仍然存在问题。其中之一是，动态的实施在概念上有些不自然，而且技术上很复杂。 这样的直接结果是无法将环量子重力与自旋泡沫完全联系起来，这是环路量子重力的路径积分版本。解决此问题的一种方法是使用一般相对性的自偶式表述。从经典的角度来看，在自偶式表述中，动力学尽可能简单。 但是，过去，存在一个障碍，阻止了基于自偶式表述的量子理论的严格定义：一个人不知道如何构建一种可接受的内部产物在国家之间的“重叠”概念，这对于从理论中提取预测至关重要。 该项目的目的是找到一种用于自动循环量子重力的内部产品。 提供了许多内部产品，包括文献中已经提到的量规和差异不变的产品，以及PI引入的类。 关键问题是它们中的任何一个是否实现了自偶偶有理论的正确现实条件 - 也就是说，这些中的任何一个是否如此，以至于经典层面上的复杂结合在量子层面上延伸到Hermitian共轭。 如果PI成功地找到了可接受的内部产品，则PI将尝试在新创建的自动划分框架中重现量子几何形状，然后尝试构建简化的汉密尔顿约束。 然后，PI将查看简化的汉密尔顿约束是否允许环量子重力与自旋泡沫模型更直接相关。