Canonical quantization in a spinor substructure of Minkowski space

Abstract

We factorize the space-time coordinates of Minkowski space into Weyl spinors with components in a split Clifford algebra. Poisson brackets are defined for spinor-valued canonical variables and applied to the quantization of point particles and strings. In particular, we obtain the Lorentz algebra for the quantum string, and show that the string supports both integral and half-integral spin states. The Clifford algebra is augmented with the octonions through an R-algebra tensor product, and we apply the results of Manogue, Schray and Dray on octonionic Lorentz transformations to obtain a Lorentz invariant string action in ten dimensions.