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De Sitter symplectic spaces and their quantizations

Published online by Cambridge University Press:  24 October 2008

J. H. Rawnsley
J. H. Rawnsley
Affiliation:
Mathematics Institute, Oxford and Mathematisches Institut, Bonn†
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Extract

The de Sitter group, Spin (4, 1), is a simply connected, semi-simple, ten-dimensional Lie group which can be contracted to the inhomogeneous Lorentz group. Physical systems with the de Sitter group as asymmetry group should resemble those of the inhomogeneous Lorentz group and may provide an alternative to these systems of special-relativistic physics. Details of physics in de Sitter space from the group theoretical view-point are given in (3). The de Sitter group is also known to be a symmetry group for the bound states of the hydrogen atom, and recent work has shown how this group acts on the corresponding classical system, the Kepler problem. See (8).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 473 - 480
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Artin, E.Geometric Algebra (Interscience, 1957).Google Scholar
(2)Chevalley, C.Algebraic Theory of Spinors (Columbia University Press, 1954).Google Scholar
(3)Hannabuss, K. C.Localizability of particles in de Sitter space. Proc. Cambridge Philos. Soc. 70 (1971), 283–302.CrossRefGoogle Scholar
(4)Karoubi, M.Algèbres de Clifford et K-thé. Ann. Sci. École. Norm. Sup (4), 1 (1968), 161–270.Google Scholar
(5)Kostant, B.Quantisation and unitary representations in Lectures in Modern Analysis and Applications III. Springer Lecture Notes 170 (1970).Google Scholar
(6)Renouard, P. Variétés symplectiques et quantification (These (1969), Orsay).Google Scholar
(7)Souriau, J. M.Structures des Systèmes Dynamiques (Dunod, 1970).Google Scholar
(8)Souriau, J. M. Sur la variété de Kepler. To appear in theproceedings of the Convegno di Geometria simplettica e Fisica matematica, Rome, January 1973 (Symposia Mathematica series, Academic Press).Google Scholar
(9)Takahashi, R.Sur les représentations unitaires des groupes de Lorentz généralisés. Bull. Soc. Math. France 91 (1963), 289–433.Google Scholar