Canonical quantization in a spinor substructure of Minkowski space

TL;DR

This paper develops a novel approach to quantizing particles and strings in Minkowski space using spinor and Clifford algebra structures, resulting in a Lorentz invariant string theory supporting various spin states.

Contribution

It introduces a new factorization of Minkowski space coordinates into Weyl spinors with Clifford algebra, and extends to octonionic structures for a Lorentz invariant ten-dimensional string action.

Findings

Derived Lorentz algebra for quantum string

Supported both integral and half-integral spin states

Established Lorentz invariance in ten-dimensional string model

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.