Abstract. 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.

PACS numbers: 0210V, 1130P

Print publication: Issue 1 (January 1996)
Received 3 July 1995, in final form 10 October 1995