The general classical solution of the superparticle

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 $\Cl(9,1)$. 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.

11 pages, REVTeX

References in corpus (2)

• The Superparticle and the Lorentz Group
• Finite Lorentz Transformations, Automorphisms, and Division Algebras

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