Abstract
Analytical expressions for the matrices and an explicit algorithm for computing Clebsch-Gordan coupling coefficients are given forsu(4) in au(3)-coupled basis as an example of the construction for anysu(n) in au(n−1) basis. The results areinduced from the known results foru(3) by means of the vector-coherent-state (VCS) theory of induced representations. The important recent result that makes this possible is the discovery that a complete set of shift tensors for the finitedimensional representations of reductive Lie algebras can be induced, by VCS methods, from those of suitably defined subalgebras.
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References
D. J. Rowe,J. Math. Phys. 25, 2662 (1984). D. J. Rowe, G. Rosenteel, and R. Carr,J. Phys. A: Math. Gen. 17, L399 (1984); D. J. Rowe, G. Rosensteel, and R. Gilmore,J. Math. Phys. 26, 2787 (1985). K. T. Hecht,The Vector Coherent State Method and Its Application to Problems of Higher Symmetries (Springer, Berlin, 1987).
D. J. Rowe and J. Repka,J. Math. Phys. 32, 2614 (1991).
D. J. Rowe and J. Repka,J. Math. Phys. 36, 2008 (1995).
D. J. Rowe and J. Repka,J. Math. Phys. (in press).
E. P. Wigner,Group Theory (Academic, New York, 1959).
M. Moshinsky,Rev. Mod. Phys. 34, 813 (1962).
K. T. Hecht,Nucl. Phys. 62, 1 (1965).
J. P. Draayer and Y. Akiyama,J. Math. Phys. 14, 1904 (1973); Y. Akiyama and J. P. Draayer,Comput. Phys. Commun. 5 405 (1973).
E. P. Wigner,Gruppentheorie (Vieweg, Braunschweig, 1931). C. Eckart,Rev. Mod. Phys. 2, 305 (1930); A. P. Stone,Proc. Camb. Phys. Soc. 57, 460 (1961).
A. R. Edmonds,Proc. R. Soc. London A268, 436 (1963).
G. E. Baird and L. C. Biedenharn,J. Math. Phys. 4, 1449 (1963),5, 1730 (1964). L. C. Biedenharn, A. Giovannini, and J. D. Louck,Commun. Math. Phys. 8, 691 (1967).
L. C. Biedenharn and J. D. Louck,Commun. Math. Phys. 8, 89 (1968). J. D. Louck,Am. J. Phys. 38, 3 (1970). J. D. Louck and L. C. Biedenharn,J. Math. Phys. 11, 2368 (1970).
K. T. Hecht, R. Le Blanc, and D. J. Rowe,J. Phys. A 20, 2241 (1987).
I. M. Gel'fand and M. L. Tseitlin,Dokl. Akad. Nauk. 71, 825, 1017 (1950).
Orthogonalization of a set of nonorthogonal vectors can be carried out by the well-known Gram-Schmidt method or, more easily, by the methods of D. J. Rowe,J. Math. Phys. 10, 1774 (1969).
K. T. Hecht and S. C. Pang,J. Math. Phys. 10, 1571 (1969).
F. Iachello and A. Arima,The Interacting Boson Model (Cambridge University Press, Cambridge, 1987). J. P. Elliott and J. A. Evans,Phys. Lett. 101B, 216 (1981).
D. J. Milliner,J. Math. Phys. 19, 1513 (1978).
H. de Guise and D. J. Rowe,J. Math. Phys. 36, 6991 (1995); and in preparation.
D. J. Rowe,Rep. Prog. Phys. 48, 1419 (1985).
D. J. Rowe, R. Le Blanc, and J. Repka,J. Phys. A 22, L309 (1989); D. J. Rowe, M. G. Vassanji, and J. Carvalho,Nucl. Phys. A 504, 76 (1989).
D. J. Rowe,J. Math. Phys. 35, 3163 (1994), D. J. Rowe and K. T. Hecht,J. Math. Phys. 36, 4711 (1995).
J. D. Vergados,Nucl. Phys. A 111, 681 (1968).
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Rowe, D.J., Repka, J. The representations and coupling coefficients of su(n); application to su(4). Found Phys 27, 1179–1209 (1997). https://doi.org/10.1007/BF02551440
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DOI: https://doi.org/10.1007/BF02551440