Gauge Theories and Quantum Gravity

规范理论和量子引力

• 批准号: 9016-2013
• 负责人: Gegenberg, Jack
• 金额: $ 1.31万
• 依托单位: University of New Brunswick
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633341
• 关键词: Gauge; Theories; Quantum; Gravity

At the frontier of theoretical physics lies the task of reconciling gravity with elementary particle physics. One effective way to make progress in this difficult problem is the development of toy models for the interaction of gravity with matter in a quantum theory. These models often have fewer space dimensions than the three of our real world; this makes them easier to manipulate mathematically. Ideally, this gives us answers to questions in this setting that are at present unattainable in more realistic theories. Over the next few years I intend to pursue three projects in this area. The first project is a re-formulation of one promising theory, string theory, one of the premier ways to to reconcile gravity and elementary particle physics. String theories as usually formulated require more than three dimensions. This is both a strength and a weakness- the former because the extra dimensions might be associated with the unification of the fundamental interactions; the latter because there has been no satisfactory resolution of the unobservability of the extra dimensions. In my work on this problem, I have the string evolve in a world where there is dust evolving as well, and this permits a world with 3 space dimensions. In my second project, I will use a mathematical tool, the Yang-Mill flow, which is related to the heat equation, in that it uniformizes the flowing quantity. I will use the Yang-Mills flow to probe the spacetime foam picture of quantum gravity in which at very small distances, the structure of spacetime fluctuates wildly. The Yang-Mills flow will show how the spacetime foam smooths out at larger distance scales to yield the more uniform spacetime structure predicted by Einstein's theory of gravity. In my final project, I probe a universe that is spherically symmetric- say far from all bits of matter, where gravity can be described by a theory in a world of one space dimension. I will use a construction that enables one to simply describe the interaction of matter with spherically symmetric gravity to explore the formation of a black hole, its decay and its eventual end point.

理论物理的前沿任务是调和重力和基本粒子物理。在这一难题上取得进展的一个有效方法是开发量子理论中重力与物质相互作用的玩具模型。这些模型的空间维度通常比我们现实世界中的三个空间维度要少；这使得它们更容易在数学上操作。理想情况下，这给了我们在这种背景下的问题的答案，这些问题目前在更现实的理论中是无法实现的。在接下来的几年里，我打算在这一领域开展三个项目。第一个项目是对一个很有前途的理论--弦理论的重新表述，弦理论是协调重力和基本粒子物理的主要方法之一。弦理论通常需要三个以上的维度。这既是长处，也是短处--前者是因为额外的维度可能与基本相互作用的统一有关；后者是因为额外维度的不可观测性没有得到令人满意的解决。在我对这个问题的研究中，我让弦在一个也有尘埃演化的世界中进化，这允许一个具有3个空间维度的世界。在我的第二个项目中，我将使用一个数学工具，杨-密尔流，它与热方程有关，因为它使流动量均匀。我将使用杨-米尔斯流来探测量子引力的时空泡沫图像，在这个图像中，在很短的距离内，时空的结构会发生剧烈的波动。杨-米尔斯流将展示时空泡沫如何在更大的距离尺度上平滑，从而产生爱因斯坦引力理论预测的更均匀的时空结构。在我的最后一个项目中，我探索了一个球对称的宇宙--比方说远离所有物质，在那里引力可以用一个空间维度的理论来描述。我将使用一种结构，使人们能够简单地描述物质与球对称重力的相互作用，以探索黑洞的形成、衰变和最终终点。