On the relationship between Twistors and Clifford algebras |
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Authors: | R. Ablamowicz N. Salingaros |
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Affiliation: | (1) Department of Mathematics, Gannon University, 16541 Erie, PA, USA;(2) Division of Mathematics, Computer Science, and Systems Design, University of Texas, 78285 San Antonio, TX, USA |
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Abstract: | Basis p-forms of a complexified Minkowski spacetime can be used to realize a Clifford algebra isomorphic to the Dirac algebra of 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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