粒子物理的拓扑模型及其在量子时空非交换性中的应用

项目名称： 粒子物理的拓扑模型及其在量子时空非交换性中的应用

项目编号： No.11505143

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： Niels Gijsbertus Gresnigt

作者单位： 西交利物浦大学

项目金额： 17万元

中文摘要： 本项目将通过替换标准模型（由具有拓扑信息的扩展对象构成）的点粒子，开发一种基本粒子及其相互作用的拓扑模型。我们通过文献了解到，支撑标准模型的Poincare-Heisenberg对称不具有任何物理相关的李代数所预期的稳定性。稳定形式的对称普遍性在点粒子意义上不再适用。.我们的工作包括并扩展了之前的拓扑模型，尤其是量子化磁通管模型、拓扑电磁模型以及helon模型（其中基本粒子对应于包括3个散带的辫）。本研究的主要目的在于，通过关联这些不同的研究项目，开发出一种综合统一的粒子物理学理论。在我们的模型中，基本粒子的属性源自展对象的拓扑学和几何学，其相互作用和内部对称按照拓扑过程理解。.我们将此模型纳入背景无关的量子引力理论, 通过量子引力状态识别我们模型中的纽结，来定量研究了量子时空不可交换性对于由包含SPHA对称的量子引力提议所预测角动量的依存性。.因此，本项工作是迈向物质和时空统一理论。

中文关键词： 粒子物理；标准模型；拓扑学；扭结理论；量子引力

英文摘要： This project will develop a topological model of elementary particles and their interactions by replacing the point particles of the Standard Model by extended objects that carry topological information. Our work is motivated from an observation in the literature that the Poincare-Heisenberg symmetry that underlies the standard model does not carry the stability that should be expected of any physically relevant Lie-algebra. A generalization of the symmetries to a stabilized version implies the notion of a point particle is no longer tenable...Our work incorporates and extends earlier topological models, in particular quantized flux tubes models, topological electromagnetism, and the helon model in which elementary particles correspond to braids consisting of three ribbons. The primary purpose of this research is to develop a comprehensive unified theory of particle physics by relating these different research programs. In our model, the properties of elementary particles are derived from the topology and geometry of the extended objects and their interactions and internal symmetries are understood as topological processes. ..We identify the elementary particles of the standard model with knotted and quantized flux tubes. We relate these to the ribbon braids of the helon model by considering the ribbons to be physical flux tubes. The closure of a braid then gives rise to a knotted or linked quantized flux tubes. ..We embed this model into background independent theories of quantum gravity. The links established between the braided ribbons and quantized knotted flux tubes allows us to develop the existing idea in the literature that suggest the standard model is an emergent property of quantum spacetime by investigating how such knotted flux tubes arise naturally from the physical vacuum. In so doing we provide a physical mechanism by which braided ribbons can be created inside an unbraided ribbon network. ..Finally we study quantitatively the dependence of quantum spacetime non-commutativity on the expectation value of angular momentum predicted in quantum gravity proposals that carry SPHA symmetry by identifying the knots in our model with the quantum gravitational states. ..This work thus provides a step towards a unified theory of matter and spacetime.

英文关键词： Particle Physics;Standard Model;Topology;Knot Theory;Quantum Gravity