标题： 超粒子的一般经典解 显示英文标题

标题： The general classical solution of the superparticle

摘要： 在基于 Clifford 代数$\Cl(9,1)$的八元数表示的完全八元数形式体系中，引入了 9+1 维时空中的向量和旋量理论。 高阶 Grassmann 层次上 CBS 超粒子的经典运动方程的通解被给出。 为了构造描述超粒子的超空间变量，旋量和向量被组合成一个$3 \times 3$Grassmann、八元数、Jordan 矩阵。 费米变量和玻色变量的洛伦兹变换和超对称变换可以用 Jordan 积的形式表达。 显示英文摘要

摘要： The theory of vectors and spinors in 9+1 dimensional spacetime is introduced in a completely octonionic formalism based on an octonionic representation of the Clifford algebra $\Cl(9,1)$. The general solution of the classical equations of motion of the CBS superparticle is given to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$ Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The combined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.