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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=521210
• 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.

在理论物理学的前沿，有一项任务是使引力与基本粒子物理学相协调。 在这个难题上取得进展的一个有效方法是在量子理论中发展引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真实的世界的三维空间维度要少，这使得它们更容易在数学上进行操作。 理想的情况是，这给了我们在这种情况下目前在更现实的理论中无法实现的问题的答案。 在未来几年里，我打算在这一领域开展三个项目。 第一个项目是重新制定一个有前途的理论，弦理论，一个首要的方法来协调重力和基本粒子物理学。弦理论通常需要三维以上的空间。 这既是优点也是缺点--前者是因为额外维度可能与基本相互作用的统一有关;后者是因为对于额外维度的不可观测性还没有令人满意的解决办法。 在我对这个问题的研究中，我让弦在一个尘埃也在进化的世界中进化，这就允许了一个三维空间的世界。 在我的第二个项目中，我将使用一个数学工具，杨-米尔流，它与热方程有关，因为它使流量均匀化。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，在非常小的距离上，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，以产生爱因斯坦引力理论所预测的更均匀的时空结构。 在我的最后一个项目中，我探测了一个球对称的宇宙--比如说远离所有物质的宇宙，在那里，引力可以用一个一维空间世界的理论来描述。 我将使用一种构造，它使人们能够简单地描述物质与球对称引力的相互作用，以探索黑洞的形成，它的衰变和它的最终终点。