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Aspects Of SU2 × ϕn Liouvillian Duality and SU2/SO(3) × (ϕ12 A5) Symmetry Over Spin (Spin-Isomorphic) Spaces Of MO-NMR and Ouantum-Rotational Tunnelling Problems

  • J. P. Colpa
  • F. P. Temme
Conference paper

Abstract

Multiple quantum NMR spin cluster problems are best understood in terms of their dual Liouvillian bases which for Ii=1/2 clusters may be realised over a simply-reducible carrier space H, spanning Hv subsets, of the irreducible representations of SU2 and ϕn; a induced symmetry and Liquvillian genealogy over Hy subspaces is given. Realization of Ok(U) x Γ[..], and of equivalent maps under SU2 x ϕ12↓A5), are shown t0 significant in treating spin cluster problems, inducing the MO-NMR of [BH]= 12 and certain corresponding quantum-rotational tunnelling problems which may be studied by inelastic spin-dependent neutron scattering techniques.

PACS No.

33.F 03.65F 760.60L 

References

  1. 1]
    F.P. Temme, Physica A162 1989 111; ibid., A166 1990 (in press)(VII).ADSCrossRefMathSciNetGoogle Scholar
  2. 2]
    P. Ooubilet, G.C. Rota & J. Stein, Stud. Appl. Maths, 53 1974 185.Google Scholar
  3. 3]
    F.P. Temme, Chem. Phys. 132 1989 9.ADSCrossRefMathSciNetGoogle Scholar
  4. 4]
    J.M. Levy-Leblond & M. Levy-Nahas;, J. Math. Phys., 6 1964 1372.ADSCrossRefMathSciNetGoogle Scholar
  5. 5]
    F.P. Temme, Molec. Phys. 66 1989 1975; Physica A166 1990 (in press)(VII).CrossRefMathSciNetGoogle Scholar
  6. 6]
    B.C. Sanctuary & F.P. Temme Molec. Phys. 55 1985 1049; ibid., 58 1986 659.ADSCrossRefGoogle Scholar
  7. 7]
    U. Press, ‘Single Particle Rotations in Mol. Cryst.’, (Vol.92, Springer.Google Scholar
  8. 8]
    G. James & A..Kerber, ‘Representation Theory of the 5 Group’, C.U.P.Google Scholar
  9. 9]
    F.P. Temme, presented: at Turku Quantum Rotational Tunnelling Sympos., 1988.Google Scholar
  10. 10]
    see A. Huller, A. Heidemann: in “Quantum aspects of Molec. Solids” 1987.Google Scholar
  11. 11]
    F.P. Temme, (to be published); see ref 1(b).Google Scholar
  12. 12]
    L.C. Biedenharn & J.O. Louck, in The Permutation group in Physics….Google Scholar
  13. 13]
    M. Mehring, Bull. Magn. Reson., 3 1978 83.Google Scholar
  14. B.C. Sanctuary, Molec. Phys., 55, 1985 1917.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. P. Colpa
    • 1
  • F. P. Temme
    • 1
  1. 1.Dept. of ChemistryQueen’s UniversityKingstonCanada

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