粒子物理的拓扑模型及其在量子时空非交换性中的应用

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.

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。

本项目涉及通过携带拓扑信息的量来描述基本粒子的物理性质和交互的可能性。特别是本项目专注于根据某一类框架辫提出的基本物质拓扑描述。Helon辫模型与LQG兼容，并且可以提供一种将SM与量子时空统一的可能方法。..本项目的研究已在国际知名且同行评审的期刊上发表了三篇文章[1,2,3]，另一篇目前仍在审核中[4]。该研究还在众多国际会议上进一步提出，产生了四篇会议记录和文献[5,6,7,8]，而第五篇会议记录和文献被接受并很快出现在了互联网上[9]。最后，该项研究已经产生了众多新的合作和研究思想，内容涉及从可除代数和约当代数到圈量子宇宙学的各种主题。..有人提议研究量子化的通量管和框架辫，希望能确认这两点。在前面的描述中，当用纽结量子化通量管确认基本粒子时，电荷的概念不再重要，而必须从电磁场中找到理论推导。在本项目早期阶段的研究表明，仅磁场的电磁相互作用可能并未明确地引入电荷[1]。因此，这些场是唯一的基本实体。..在第二篇论文中，基于一个量子群SUq(3)味对称性的新电荷特定八元数和十重态重子质量公式被推导出来[2]。对于八元数和十重态重子质量，推导出的质量关系误差仅为0.02%和0.08%。量子群对熟悉的对称概念做了概括，并且与纽结和辫密切相关[6,7]。此外，相同的量子群还被用于研究重子的磁矩[10]。 ..作为框架辫的费米子拓扑模型与标准模型对称性的可除代数描述之间的意外结构相似性被发现出来。使用复数和四元数表示的非普通辫群，恰好是那些可以构造单代辫费米子的。反过来，这也使得helon模型的辫物质状态与八元数代数[3]相关联。使用特殊的约当代数[9]将辫模型从一代扩展至三代，因此也取得了一些进展[9]。