Abstract
Real and complex spinors in ten dimensions are considered as elements of left minimal ideals in C19,1 and C19, 2 respectively. It is shown that the real spinors form a space of dimension eight over an algebra of split quaternions while the complex spinors form a space of dimension eight over a singular division algebra. Properties of bilinear forms on both spaces are discussed and a comparison is made with spinors in dimension four. Explicit spinor bases are computed using CLICAL.
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References
Shnider S. 1988 ‘The superconformai algebra in higher dimensions’ Lett. Math. Phys 16 377–383
Foot R. and Joshi G.C. 1988 ‘Remark concerning the twistor formulation of a massless particle and the division algebras’ Lett. Math. Phys 16 77–82
Kwon P. and Villasante M. 1989 ‘Decomposition of the scalar superfield in ten dimensions’ J. Math. Phys 30 201–212
Hughston, L.P. and Shaw, W.T. (1987) ‘Classical strings in ten dimensions’, Preprint, Lincoln College, Oxford 0X1 3DR, England.
Wene G.P. 1984 ‘A construction relating Clifford algebras and Cayley-Dickson algebras’ J. Math. Phys 25 2351–2353
Hagmark, P.-E. and Lounesto, P. (1986) ‘Walsh functions, Clifford algebras and Cayley-Dickson process,’ in J.S.R. Chisholm and A.K. Common (eds.), Clifford Algebras and Their Applications in Mathematical Physics, D. Reidel, ordrecht, 531–540.
Lambert, D. (1988) ‘Modèles Sigma Pseudo-Riemanniens: Le Role des Algèbres de Cayley-Dickson et de Clifford,’ Ph.D. Dissertation, Université Catholique de Louvain.
Sorgsepp L. and Lohmus J. 1979 ‘About nassociativity in physics and Cayley-Graves—octonions’ Hadronic J 2 1388–1459
Lounesto, P. and Wene, G.P. (1987) ‘Idempotent structure of Clifford algebras’, Acta Applicandea Mathematicae 9, 165–173.
Lounesto, P., Mikkola, R., and Vierros, V. (1989) Clical — Complex Number, Vector, Spinor and Clifford Algebra Calculations for MS-DOS Personal Computers, ver. 3.0, Helsinki University of Technology, Institute of Mathematics, SF-02150 Espoo, Finland.
Lam, T.-Y. (1973) The Algebraic Theory of Quadratic Forms, Benjamin, Reading.
Salingaros, N. and Ilamed, Y. (1981) ‘Algebras with three anticommuting elements. I. Spinors and quaternions’, J. Math. Phys. 22, 2091–2095.
Salingaros, N. (1981) ‘Algebras with three anticommuting elements. II. Two algebras over a singular field’, J. Math. Phys. 22, 2096.
Lounesto, P. (1981) ‘Scalar products of spinors and an extension of Brauer-Wall groups’, Found. Phys. 11, 721.
Crumeyrolle, A. (1974) Algebres de Clifford et Spineurs, Université Paul Sabatier, Toulouse.
Bugajska, K. (1986) ‘Geometrical properties of the algebraic spinors for R3,1, J. Math. Phys. 27, 143–150.
Ablamowicz, R., Lounesto, P. and Maks, J. (1991) ‘Report on the “Second Workshop on Clifford Algebras and Their Applications in Mathematical Physics,”’ Université des Sciences et Techniques du Languedoc, Montpellier, France, September 1989. Found. Physics, 21, 735–748.
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© 1992 Springer Science+Business Media Dordrecht
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Ablamovicz, R. (1992). Algebraic spinors for R9,1 . In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_2
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DOI: https://doi.org/10.1007/978-94-015-8090-8_2
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