On the relationship between twistors and Clifford algebras (Q1076110)

Let C be the Clifford algebra associated with the complexification of a Minkowski space-time M, so that C is the ring of 4 by 4 complex matrices, and let S be the spinor space of C, that is, a minimal left ideal. The authors define a ''space of index one twistors'' to be S together with the natural representation of the conformal group of M via C. There is an isomorphism between \(S\otimes S\) and C which the authors refine to give the symmetric and antisymmetric parts of \(S\otimes S\) in terms of the grading in C; this permits an interpretation of the formalism of skew products of twistors in terms of the product in the Clifford algebra.