粒子拓扑、编织和编织带
Particle Topology, Braids, and Braided Belts
摘要：
最近的工作表明，某些量子引力理论的拓扑特征可以被解释为粒子，与标准模型中已知的第一代费米子和玻色子相匹配。这是通过识别拓扑结构与三股上的框架Artin辫群的元素，并证明用于将这些辫的不变量之间的对应关系来实现的（辫子是一组不相交的曲线，其将一组$N$点与另一组$N$点连接），以及诸如电荷，色荷，在本文中，我们展示了如何操纵一个修改形式的框架辫子，以产生一个不变的标准式的同构辫子集，其特征在于由一个向量的实数。这将作为在未来工作中更完整地讨论量子数的基础。
英文摘要：
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying topological structures with elements of the framed Artin braid group on three strands, and demonstrating a correspondence between the invariants used to characterise these braids (a braid is a set of non-intersecting curves, that connect one set of $N$ points with another set of $N$ points), and quantities like electric charge, colour charge, and so on. In this paper we show how to manipulate a modified form of framed braids to yield an invariant standard form for sets of isomorphic braids, characterised by a vector of real numbers. This will serve as a basis for more complete discussions of quantum numbers in future work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
