Publication: Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras
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2008
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IOP Publishing Ltd
Abstract
We show that the Inönü-Wigner contraction naturally associated to a reduction chain s ⊃ s' of semisimple Lie algebras induces a decomposition of the Casimir operators into homogeneous polynomials, the terms of which can be used to obtain additional mutually commuting missing label operators for this reduction. The adjunction of these scalars that are no more invariants of the contraction allow to solve the missing label problem for those reductions where the contraction provides an insuflcient number of labelling operators.
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THE 5TH INTERNATIONAL SYMPOSIUM ON QUANTUM THEORY AND SYMMETRIES 22–28 July 2007, Valladolid, Spain
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[1]Okubo S 1962 Prog. Theor. Phys. 27 949
Goldberg H and Lehrer-Ilamed Y 1962 J. Math. Phys. 4 501
Burakovsky L and Horwitz L P 1997 Found. Phys. Lett. 10 131
Burakovsky L and Goldman T 1997 hep-ph/9708498
[2]Süalp G and Kaptanoglu S 1983 Ann. Phys. 147 460
Kitazawa N 1994 Tumbling and Technicolor Theory DPNU-94-03 (Nagoya: Japan)
[3]Iachello F and Arima A 1987 The interacting boson model (Cambridge Univ. Press, Cambridge)
[4]Elliott J P 1958 Proc. R. Soc. Lond. A 245 128 562
Bargmann V and Moshinsky M 1965 Nucl. Phys. 23 177
Green H S and Bracken A J 1974 Int. J. Theor. Phys. 11 157
Judd B R, Miller W, Patera J and Winternitz P 1974 J. Math. Phys. 15 1787
Sharp R T 1975 J. Math. Phys. 16 2050
Quesne Ch 1976 J. Math. Phys. 17 1452
1977 18 1210
De Meyer H, Vanden Berghe G, Van der Jeugt J and De Wilde P 1985 J. Math. Phys. 26 2124
Rowe D J, Le Blanc R and Repka J 1989 J. Phys. A: Math. Gen. 22 L309
Hecht K T 1994 J. Phys. A: Math. Gen. 27 3445
Turner P S, Rowe D J and Repka J 2006 J. Math. Phys. 47 023507
[5]Peccia A and Sharp R T 1976 J. Math. Phys. 17 1313
[6]Wigner E P 1937 Phys. Rev. 51 106
Lipkin H J 1964 Phys. Rev. Lett. 13 590
Khanna F C and Umezawa H 1994 Chinese J. Phys. 32 1317
von Isacker P and Juillet O 1999 Nucl. Phys. A 564 739
Valencia J P and Wu H C 2004 Braz. J. Phys. 34 837
[7]Campoamor-Stursberg 2007 J. Phys. A: Math. Theor. to appear hep-th/arXiv:0706.2581
[8]Vitiello G and de Concini C 1976 Nucl. Phys. B 116 141
Anderson J T 1981 Phys. Rev. D 23 1856
Celeghini E, Tarlini M and Vitiello G 1984 Nuovo Cimento A 84 19
[9]Campoamor-Stursberg R 2006 J. Phys. A: Math. Gen. 39 2325
Campoamor-Stursberg R 2007 J. Phys. A: Math. Theor. 40 5355
[10]Segal I E 1951 Duke Math. J. 18 221
Inönü E and Wigner E P 1953 Proc. Nat. Acad. Sci USA 39 510
Domokos G and Tindle G L 1968 Commun. Math. Phys. i 7 160
[11]Campoamor-Stursberg R 2003 J. Phys. A: Math. Gen. 36 1357
[12]Van der Jeugt 1984 J. Math. Phys. 25 1221
[13]De Meyer H, Vanden Berghe G and De Wilde P 1987 Comput. Phys. Comm. 44 197
[14]Hughes J W B and Van der Jeugt J 1985 J. Math. Phys. 26 894
[15]Rosensteel G 1977 Int. J. Theor. Phys. 16 63
Graber J L and Rosensteel G 2003 Phys. Rev. C 68 014301
[16]Gaskell R, Rosensteel G and Sharp R T 1981 J. Math. Phys. 22 2732
[17]Barut A O 1972 in The Structure of Matter (Proc. Rutherford Centennial Symp., 1971) (Christchurch, New Zealand)
[18]Rumer Yu B and Fet A I 1971 Teor. Mat. Fiz. 9 203
Konopel'chenko B G and Rumer Yu B 1979 Uspekhi Fiz. Nauk 129 339
Byakov V M, Kulakov Yu I, Rumer Yu B and Fet A I 1976 Preprint ITEP-26, ITEP-90
Kibler M R 1989 J. Mol. Struct. 187 83
Carlson C M, Hefferlin R A and Zhuvikin G V 1995 Analysis of Group Theoretical Periodic Syst. Molecules using Tabulated Data Joint Report SC/SPBU-2
Kibler M R 2004 The Mathematics of the Periodic Table ed D H Rouvray and R B King (Baldock: Research Studies Press)
[19]Kibler M R 2004 Mol. Phys. 102 1221
[20]Kibler M R private communication
[21]Racah G 1949 Phys. Rev. 76 1352
Racah G 1951 Group Theory and Spectroscopy (Princeton Univ. Press, New Jersey)
Fano U and Racah G 1959 Irreducible tensorial Sets (Academic Press: New York)
[22]Partensky A and Maguin C 1978 J. Math. Phys. 19 511
[23]Frank A and van Isacker P 1994 Algebraic Methods in Molecular and Nuclear Structure Physics (Wiley: New York)
Iachello F and Levine R D 1995 Algebraic Theory of Molecules (Oxford Univ. Press: Oxford)