Remark concerning the twistor formulation of a massless particle, and the division algebras

Abstract

A possible generalization of the twistor description of a massless particle to spacetime dimensions other than four is investigated. While the description of a massless particle's momentum in terms of a spinor is possible in spacetime dimensions of 3, 4, 6, and 10, the description of the angular momentum of the particle cannot be generalized from the four-dimensional case to six or ten dimensions in any straightforward manner. The possible generalization sought utilizes the \({\text{SL(2,}}\mathbb{A}{\text{),}}\mathbb{A} = \mathbb{R},\mathbb{C},\mathbb{Q},\mathbb{O}\) formulation of the covering group of the Lorentz group in D=3, 4, 6, and 10 dimensions. This formulation is reviewed and further developed here.