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The localizability of particles in de Sitter space

Published online by Cambridge University Press:  24 October 2008

K. C. Hannabuss
K. C. Hannabuss
Affiliation:
Mathematical Institute, Oxford
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Abstract

Motivated by the Iwasawa decomposition and its geometrical interpretation, two new decompositions of the de Sitter group are obtained. The first is applied to construct the representations of the de Sitter group in a form immediately comparable with those of the Poincaré group. In particular they act on functions over an hyperboloid like the momentum hyperboloid of the Poincaré group, although they require both positive and negative mass shells of that hyperboloid. Using the second decomposition it is shown that the representations of the de Sitter group are localizable in the sense of Mackey and Wightman. Position operators are exhibited.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 283 - 302
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Bakri, M. M.Nuovo Cimento A 51 (1967), 864–869.CrossRefGoogle Scholar
(2)Bander, M. and Itzykson, C.Rev. Modern Phys. 38 (1966), 330–358.CrossRefGoogle Scholar
(3)Dirac, P. A. M.Ann. of Math. 36 (1935), 657–669.CrossRefGoogle Scholar
(4)Dixmier, J.Bull. Soc. Math. France 89 (1961), 9–41.CrossRefGoogle Scholar
(5)Gel'faitd, I. M., Graev, M. I. and Vilenkin, N. Ya.Generalised Functions, Volume 5, Integral geometry and representation theory (Academic Press, New York, 1966).Google Scholar
(6)Mackey, G. W.Bull. Amer. Math. Soc. 69 (1963), 628–686.CrossRefGoogle Scholar
(7)Mackey, G. W.Induced representations of groups and quantum mechanics (W. A. Benjamin Inc., New York, Amsterdam; and Editore Boringhieri, Torino, 1968).Google Scholar
(8)Newton, T. D. and Wigner, E. P.Rev. Modern Phys. 21 (1949), 400–406.CrossRefGoogle Scholar
(9)Philips, T. and Wigner, E. P.In Group Theory and Its Applications, ed. Loeb, E. M. (Academic Press, New York, 1968).Google Scholar
(10)Robertson, H. P. and Noonan, T. W.Relativity and Cosmology (W. B. Saunders Company, Philadelphia, 1968).Google Scholar
(11)Takahashi, R.Bull. Soc. Math. France 91 (1963), 289–433.CrossRefGoogle Scholar
(12)Wightman, A. S.Rev. Modern Phys. 34 (1962), 845–872.CrossRefGoogle Scholar
(13)Wigner, E. P.Ann. of Math. 40 (1939), 149–204.CrossRefGoogle Scholar