Homotopy theory and quantum gravity

同伦理论和量子引力

• 批准号: 238498-2006
• 负责人: Christensen, JohnDaniel
• 金额: $ 1.31万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=393948
• 关键词: Homotopy; theory; quantum; gravity

My research involves topology, physics, computation, and various topics in between. Topology is the study of surfaces and higher-dimensional shapes, and the ways in which they can be stretched, deformed and mapped into each other.  A common technique is to study spaces by probing them with loops, spheres and other geometrically regular spaces.  This generally results in algebraic invariants. More recently, the ideas of topology are finding applications in other fields, such as algebra, algebraic geometry and physics.  There are many questions and techniques that make sense in all of these settings, and the main theme of my work in topology is the study of such global problems. This interplay between disciplines has proven to be extremely fruitful, and I will continue work in this direction. One of the most important unsolved problems in physics is the unification of general relativity, Einstein's highly successful theory of gravity, with quantum mechanics, which describes all the other known forces.  My work focuses on a promising approach to this problem, a theory called loop quantum gravity. Currently two of the biggest open problems in loop quantum gravity are the study of its classical limit and the ways in which matter can be introduced into the theory.  The classical limit problem asks what the large scale behaviour of the theory is, and compares it to known cosmological data. Introducing matter into the theory is important in order to learn what corrections the theory makes to the existing theory of particle physics, and to see if any of these predictions are experimentally testable. I will study these problems both analytically and through the use of computer simulations. Such work is an important test of a theory and can lead to improvements and other developments.

我的研究涉及拓扑学，物理学，计算，以及介于两者之间的各种主题。拓扑学是研究表面和高维形状以及它们可以拉伸、变形和相互映射的方式的学科。一种常见的技术是通过用环、球和其他几何规则空间来研究空间。这通常会导致代数不变量。最近，拓扑学的思想在其他领域得到了应用，如代数、代数几何和物理学。在所有这些背景下，有许多问题和技术都是有意义的，我在拓扑学领域工作的主题就是研究这些全局问题。学科之间的这种相互作用已被证明是非常富有成效的，我将继续朝着这个方向努力。物理学中最重要的未解决的问题之一是广义相对论与量子力学的统一，广义相对论是爱因斯坦非常成功的引力理论，量子力学描述了所有其他已知的力。我的工作集中在一个有希望解决这个问题的方法上，一个叫做圈量子引力的理论。目前圈量子引力理论中两个最大的问题是经典极限的研究和如何将物质引入到理论中。经典极限问题询问理论的大尺度行为是什么，并将其与已知的宇宙学数据进行比较。将物质引入到理论中是很重要的，以便了解该理论对现有粒子物理学理论的修正，并看看这些预测中是否有任何一个是可以实验检验的。我将通过分析和计算机模拟来研究这些问题。这样的工作是对一个理论的重要检验，可以导致改进和其他发展。