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Clifford algebras in general relativity

Published online by Cambridge University Press:  24 October 2008

E. A. Lord
E. A. Lord
Affiliation:
Department of Mathematics, King's College, University of London
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Summary

The generalization of the Dirac and quaternion algebras to Riemannian spaces is outlined. The components of various elements of the algebras are interpreted as physical quantities (tensors) and their symmetries and algebraic properties are linked with the properties of the algebra. The generalization of the quaternion algebra is of particular interest in that it resolves the anomalies that arise in the usual identification of quaternions with rank two spinors. Algebraic expressions for the electromagnetic energy momentum tensor, the Ricci tensor and Einstein tensor are obtained in both E-number and quaternion form. Extension of the principles to EF-numbers yields a proof of the symmetry properties of Bel's tensor and a simple expression for its divergence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 785 - 807
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bel, L.C.R. Acad. Sci. Paris 248 (1959), 1297–1300.Google Scholar
(2)Eddington, A. S. SirRelativity theory of protons and electrons (Cambridge University Press, 1936).Google Scholar
(3)Eddington, A. S. SirFundamental theory (Cambridge University Press, 1946).Google Scholar
(4)Ellis, J.Proc. Roy. Irish Acad. 64 (1966), 127–142.Google Scholar
(5)Kilmister, C. W.Proc. Roy. Soc. London Ser. A 199 (1949), 517.Google Scholar
(6)Kilmister, C. W.Proc. Roy. Soc. London Ser. A 207 (1951), 402–415.Google Scholar
(7)Kilmister, C. W. and Newman, D. J.Proc. Cambridge Philos. Soc. 55 (1959), 139–141.Google Scholar
(8)Lichnerowicz, A.C.R. Acad. Sci. Paris 247 (1958), 433.Google Scholar
(9)Rastall, P.Rev. Mod. Phys. 36 (no. 3) (1964), 820–32.CrossRefGoogle Scholar
(10)Schrödinger, E.S.B. Preuss. Acad. Wiss. (1932), 105.Google Scholar