论文标题
关于旋转器和多形式的注释II：四元组和八元
Notes on Spinors and Polyforms II: Quaternions and Octonions
论文作者
论文摘要
Pauli矩阵是2x2无跟踪的矩阵，具有真实的对角线和复杂（复杂的偶联）非对角线条目。他们生成Clifford代数CL（3）。可以通过在四元组或八元（或其拆分版本）中替换一个值的值来概括它们。这些Quaternionic和Octonionic概括分别产生Cl（5）和Cl（9）的众所周知的模型。本文的主要目的是将这些模型与创建/歼灭操作员构造产生的模型明确联系起来。我们详细描述了与四元组和八元有关的模型，以及分裂的四元组和八元。特别是，我们记录了旋转的韦尔纺纱器的描述（4,4），这些旋转旋转器似乎并未出现在文献中。
Pauli matrices are 2x2 tracefree matrices with a real diagonal and complex (complex-conjugate) off-diagonal entries. They generate the Clifford algebra Cl(3). They can be generalised by replacing the off-diagonal complex number by one taking values in either quaternions or octonions (or their split versions). These quaternionic and octonionic generalisations generate well-known models of Cl(5) and Cl(9) respectively. The main aim of the paper is to explicitly relate these models to the models arising via the creation/annihilation operator construction. We describe in details the models related to quaternions and octonions, as well as to the split quaternions and octonions. In particular, we record the description of the possible types of Weyl spinors of Spin(4,4), which does not seem to have appeared in the literature.
