International Research Fellowship Program: Computational Investigation of the Semiclassical Limit of Loop Quantum Gravity

0401966威利斯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三到二十四个月的研究。 该计划的奖项提供了联合研究的机会，以及使用独特或互补的设施，专业知识和国外的实验条件。Willis将与西安大略大学的J.丹尼尔·克里斯滕森博士合作。将爱因斯坦的引力理论（广义相对论）与量子理论相结合是理论物理学中的一个中心、基本问题，而圈量子引力是目前唯一严格定义的引力量子理论候选者。确定它是否具有正确的经典极限是这种量子引力方法的关键未决问题。这项工作试图了解的是，在最小尺度上描述空间和时间的理论，在最小尺度上必须以量子力学的方式处理引力，是否也能够描述爱因斯坦的广义相对论已经成功描述的大尺度。因此，它是对理论的重要一致性检查：它必须与经典理论一致，后者是有效的。在这个项目中，PI试图研究完整理论的半经典极限。具体来说，他建议继续在主办机构进行现有的工作，并开始其他工作，每一项工作都试图通过计算研究对环圈量子引力中产生的空间的描述--一个由顶点连接在一起的“边”组成的互连网络或晶格--是否可以在足够大的尺度上看起来像我们周围看到的光滑连续空间。我们通过数值计算来做到这一点，即连续统图像的某些特征性质，如表面的面积，是否具有来自量子理论的值，这些值非常接近于来自经典理论的值。到目前为止，简单模型的结果令人鼓舞，但在研究完整的理论之前，无法得出确切的结论。UWO提供了一个独特的机会来做到这一点，因为克里斯滕森博士的团队可能是世界上唯一一个正在进行量子引力计算方法的团队。 尽管量子引力领域作为一个整体可能是相当抽象的，涉及到许多本科生无法接触到的数学，但这项工作的计算方面是可以接触到的，并允许“动手”的方法来学习计算技术和这些技术所应用的模型的物理学。就其性质而言，这项工作必须借鉴不同的学科，从纯数学到物理学，再到计算方法，因此涉及这些领域的研究人员和学生之间的互动。

0401966WillisThe International Research Fellowship Program enables U.S. scientists and engineers to conduct three 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-two-month research fellowship by Dr. Joshua L. Willis to work with Dr. J. Daniel Christensen at the University of Western Ontario.Reconciling Einstein's theory of gravity (general relativity) with quantum theory is a central, fundamental problem in theoretical physics, and loop quantum gravity is presently the only rigorously well defined candidate quantum theory of gravity. Establishing whether or not it has the correct classical limit is the key open question for this approach to quantum gravity. What this work seeks to understand is whether the theory, which gives a description of space and time at the smallest scales where it is essential to treat the gravitational force quantum mechanically, is also able to describe the large scales already successfully described by Einstein's general theory of relativity. Thus, it is an important consistency check on the theory: it must agree with the classical theory where the latter is valid. In this project, the PI seeks to investigate the semiclassical limit of the full theory. Specically, he proposes to continue existing work at the host institution as well as to begin other work, each of which seeks to computationally investigate whether or not the description of space arising in loop quantum gravity - an interconnected network or lattice of "edges" joined together at vertices - can look on a large enough scale like the smooth continuum of space that we see around us. We do this by calculating, numerically, whether certain characteristic properties of the continuum picture, such as the areas of surfaces, have values coming from the quantum theory that are very close to those coming from the classical theory. The results from simpler models have so far been encouraging, but firm conclusions cannot be drawn until the full theory is investigated. UWO provides a unique opportunity to do this as Dr. Christensen's group there is perhaps the only one in the world where such a computational approach to quantum gravity is being carried out. Even though the field of quantum gravity as a whole can be rather abstract and involve mathematics not accessible to many undergraduates, the computational aspects of the work are accessible and allow a "hands-on" approach to learning both computational techniques and also the physics of the model to which those techniques are applied. By its nature, this work must draw on different disciplines, from pure mathematics, to physics, to computational methods, and thus involves interaction between researchers and students in these fields.