Quantum gravity and non-linear sigma models

量子引力和非线性西格玛模型

• 批准号: 9016-2008
• 负责人: Gegenberg, Jack
• 金额: $ 1.72万
• 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: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=450397
• 关键词: Quantum; gravity; non; linear; sigma

My research focuses on the problem of constructing a quantum theory which describes the interaction of fields and particles with the gravitational field. This remains THE unsolved problem in fundamental theoretical physics. My particular research program in this area involves constructing toy quantum gravity models; that is, theories which address the basic issue but are less encumbered by the profound technical difficulties associated with this problem. Typically, these toy models involve physics in which`space' has less than three dimensions. One such class of theories, quantum dilaton gravity, has only one spatial dimension. These models can be pushed quite far, and in them one can address some of the difficult issues in quantum gravity- for instance, the problem of time, the occurrence of singularities and the decay of black holes. My current work in this area proceeds from a novel procedure for constructing quantum theories, and predicts a discrete, lattice-like structure for space. Another problem that I work on concerns non-linear sigma models. String theories are a type of non-linear sigma model in which the background spacetime geometry is flat, as in the special theory of relativity. If the background is not flat, then the self-consistency of the theory requires that certain equations, called the RG flow, have fixed points and these fixed points are the permissible backgrounds. I am looking at RG flows and addressing questions concerning the relationship between these equations and the dynamical changes (that is, changes in time) of geometries and other fields. Finally, I am looking at theories which generalize conformal field theories. The latter are field theories over a two dimensional spacetime, characterized by an infinite dimensional symmetry algebra, called the Kac-Moody algebra. I am looking at generalizations which are field theories in a four dimensional spacetime, and are characterized by a certain generalizations of the Kac-Moody algebras, called 2-Toroidal Lie algebras.

我的研究重点是构建一个量子理论的问题，该理论描述了场和粒子与引力场的相互作用。 这仍然是基础理论物理学中未解决的问题。 我在这一领域的研究计划涉及构建玩具量子引力模型;也就是说，理论解决了基本问题，但较少受到与这个问题相关的深刻技术困难的阻碍。 通常，这些玩具模型涉及的物理学中的“空间”小于三维。 其中一类理论，量子引力理论，只有一个空间维度。 这些模型可以被推广到相当远的地方，在这些模型中，人们可以解决量子引力中的一些困难问题-例如，时间问题，奇点的出现和黑洞的衰变。 我目前在这一领域的工作是从构建量子理论的一个新过程出发的，并预测了空间的离散的格子状结构。 我研究的另一个问题涉及非线性sigma模型。 弦理论是一种非线性的σ模型，其背景时空几何是平坦的，就像狭义相对论一样。 如果背景不是平坦的，那么理论的自洽性要求某些称为RG流的方程具有不动点，并且这些不动点是允许的背景。 我正在研究RG流，并解决有关这些方程与几何和其他场的动态变化（即时间变化）之间关系的问题。 最后，我正在研究推广共形场论的理论。 后者是二维时空上的场论，其特征是一个无限维对称代数，称为卡茨-穆迪代数。 我正在研究四维时空中的场论的推广，其特征在于卡茨-穆迪代数的某些推广，称为2-Toroidal李代数。