Abstract
Basis p-forms of a complexified Minkowski spacetime can be used to realize a Clifford algebra isomorphic to the Dirac algebra of γ matrices. Twistor space is then constructed as a spin space of this abstract algebra through a Witt decomposition of the Minkowski space. We derive explicit formulas relating the basis p-forms to index one twistors. Using an isomorphism between the Clifford algebra and a space of index two twistors, we expand a suitably defined antisymmetric index two twistor basis on p-forms of ranks zero, one, and four. Together with the inverse formulas they provide a complete passage between twistors and p-forms.
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Ablamowicz, R., Salingaros, N. On the relationship between Twistors and Clifford algebras. Lett Math Phys 9, 149–155 (1985). https://doi.org/10.1007/BF00400713
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DOI: https://doi.org/10.1007/BF00400713