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 Cl(9, 1). The general solution of the classical equations of motion of the CBS superparticle is give n to all orders of the Grassmann hierarchy. A spinor and a vector are combined into a 3 x 3 Grassmann, octonionic, Jordan matrix in order to construct a superspace variable to describe the superparticle. The co mbined Lorentz and supersymmetry transformations of the fermionic and bosonic variables are expressed in terms of Jordan products.