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

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 2, 3, 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 SL(2, A), A=R, C, Q, 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. (orig.)