The general classical solution of the superparticle

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 . 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 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.