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Tensor operators under semi-simple groups

Published online by Cambridge University Press:  24 October 2008

A. P. Stone
A. P. Stone
Affiliation:
Department of MathematicsUniversity of Hull
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Abstract

Tensor operators under any group are defined and the theory is developed for semi-simple continuous groups. Coupled tensor operators are introduced and the matrix elements of tensor operators are expressed in terms of the coupling coefficients. The structure of generalized Casimir operators is investigated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 460 - 468
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Cartan, E.Thèse (Paris, 1894).Google Scholar
(2)Cartan, E. and Schouten, J. A.Proc. K. Akad. Wet. Amst. 29 (1926), 803.Google Scholar
(3)Casimir, H.Proc. K. Akad. Wet. Amst. 34 (1931), 844.Google Scholar
(4)Eckart, C.Rev. Mod. Phys. 2 (1930), 305.Google Scholar
(5)Edmonds, A. R.Angular momentum in quantum mechanics (Princeton, 1957).CrossRefGoogle Scholar
(6)Eisenhart, L. P.Continuous groups of transformations (Princeton, 1933).Google Scholar
(7)Koster, G. F.Phys. Rev. 109 (1958), 227.Google Scholar
(8)Lie, S.Vorlesungen über kontinuierliche Gruppen (Leipzig, 1893).Google Scholar
(9)Racah, G.Phys. Rev. 62 (1942), 438.Google Scholar
(10)Racah, G.Phys. Rev. 63 (1943), 367.CrossRefGoogle Scholar
(11)Racah, G.Phys. Rev. 76 (1949), 1352.CrossRefGoogle Scholar
(12)Racah, G.Rend. Lincei (8), 8 (1950), 108.Google Scholar
(13)Racah, G.Group theory and spectroscopy (unpublished lecture notes, Princeton, 1951).Google Scholar
(14)Rose, M. E.Elementary theory of angular momentum (New York, 1957).CrossRefGoogle Scholar
(15)Spiers, J. A.Proc. Phys. Soc. A, 68 (1955), 50.CrossRefGoogle Scholar
(16)van der Waerden, B. L.Math. Z. 37 (1933), 446.Google Scholar
(17)Weyl, H.Math. Z. 23 (1925), 271.Google Scholar
(18)Weyl, H.Math. Z. 24 (1926), 328.CrossRefGoogle Scholar
(19)Weyl, H.Math. Z. 24 (1926), 377.CrossRefGoogle Scholar
(20)Wigner, E. P.Group theory (New York, 1959).Google Scholar