粒子物理学中的八元数：广义真时结构
Octonions in Particle Physics through Structures of Generalised Proper Time
摘要：
在考虑适合描述粒子物理基本元素的基本数学结构的性质时，偶尔会提出八元数的重要作用，作为复数的扩展和唯一的最大除法代数。而不是最初基于数学美学的更抽象的理由，在这里，我们描述了一个统一的理论动机概念通过一个基本概括的表达为当地适当的时间间隔，超越了4维时空，也超越了当地结构的模型与额外的空间维度，对于这一点，明确的数学发展自然地将八元数代数作为一个基本特征。物质的性质是直接通过对称性破缺结构所必需的外部4维时空背景的提取，并再现了粒子物理学的标准模型的一系列特征结构。虽然已经采用了基于八元数的特殊李群E6和E7的结构，但完整标准模型的发现以及新的物理学超越，预计将涉及与E8相关的结构，其中八元数代数再次被认为具有根本的重要性。
英文摘要：
In considering the nature of the basic mathematical structures appropriate for describing the fundamental elements of particle physics a significant role for the octonions, as an extension from the complex numbers and uniquely the largest division algebra, has occasionally been proposed. Rather than being based initially upon the more abstract grounds of mathematical aesthetics, here we describe a unified theory motivated conceptually through an elementary generalisation of the expression for a local proper time interval, beyond that of 4-dimensional spacetime and also beyond that of the local structure of models with extra spatial dimensions, for which the explicit mathematical development naturally incorporates the octonion algebra as an essential feature. Properties of matter are identified directly through the symmetry breaking structure entailed in the necessary extraction of the external 4-dimensional spacetime background and are shown to reproduce a series of characteristic structures of the Standard Model of particle physics. While already employing octonion-based constructions of the exceptional Lie groups E6 and E7 the uncovering of the full Standard Model, as well as new physics beyond, is predicted to involve an E8-related structure for which the octonion algebra is again anticipated to be of fundamental importance.
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