The spinor string in a Clifford substructure of space-time

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 Clifford-valued canonical variables and applied to the quantization of the point particle and string. In particular, we obtain the Lorentz algebra for the quantum string, and show that the string supports both integral and half-integral spin states. Commutation and anti-commutation relations are derived for the amplitudes of the spinning string. 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.