（分裂）八元数中的狄拉克方程：起源、变体与现代背景
The Dirac equation in (split-)octonions: origins, variants, and modern context
AI总结：
综述八元数和分裂八元数表达狄拉克方程的方式，分四组介绍，阐述二因子方法起源，研究‘分裂八元数狄拉克方程’，经显式保结构旋转表明其与直积表示相同，肯定其真正贡献。
AI中文摘要：
八元数和分裂八元数已被用于以几种概念上不同的方式来表达物理学中的狄拉克方程。本综述将它们分为四组：二因子（直积）、三因子和投影表示，这些表示原生地使用（分裂）八元数基元来模拟时空基；以及八元数对作用于旋量的狄拉克代数的常规用法。文中给出了它们现代用法以及近期原生分裂八元数分析方法的指引。在二因子方法中，记录了其起源。此外，研究了M. Gogberashvili和A. Gurchumelia的‘分裂八元数狄拉克方程’，通过显式保结构旋转表明它与直积表示相同。肯定了其真正贡献。
英文摘要：
Octonions and split-octonions have been used to express the Dirac equation in physics in several conceptually distinct ways. This review organizes them into four groups: the 2-factor, 3-factor, and projection representations, which use (split-)octonion basis elements natively to model a spacetime basis, and the conventional use of octonions to carry Dirac algebra acting on spinors. For each group we identify the originating construction, relate later variants to it, and point to modern applications and to recent methods for native split-octonionic analysis. Because the multiplication table of the (split-)octonions is not unique, forms that look different in print can coincide after a norm-preserving linear isometry and a multiplication-preserving change of basis; we make such relations explicit and tabulate the basis conventions used across select sources. The 2-factor representation is treated in most detail: we document its origin and show that a recently proposed split-octonionic Dirac equation coincides with it after such an isometry and change of basis, while crediting the independent contributions of that work.
