Abstract
A new representation of a real Clifford algebra by itself is presented, which does not use onesided minimal ideals. This generalizes the “operator form” for Dirac spinors introduced by D. Hestenes. The spinor spaces obtained thus are related to a Clifford subalgebra of the parent algebra. Classification of real Clifford algebras and interior products of spinors together with their isometry groups are discussed.
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References
D. Hestenes, J. Math. Phys. 8, 798 (1967); 14, 893 (1973). See also Hestenes conference lecture, ‘Clifford algebra and the Interpretation of Quantum Mechanics’
P. Lounesto, Found. Phys. 11, 721 (1981)
There seems to be an overlapping between some of our results and those of P. Lounesto, ‘On primitive idjempotents of Clifford algebras’, Report — HTKK-MAT-A 113, (Helsinki, 1977)
I.R. Porteous, Topological geometry (Van Nostrand, London, 1969)
Proofs for the results presented here are given in A. Dimakis, dissertation (Göttingen, 1983)
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© 1986 D. Reidel Publishing Company
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Dimakis, A. (1986). A New Representation for Spinors in Real Clifford Algebras. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_4
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DOI: https://doi.org/10.1007/978-94-009-4728-3_4
Publisher Name: Springer, Dordrecht
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