Unitary Group Approach to the Many-Electron Correlation Problem

  • J. Paldus
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 24)


These lecture notes are intended to provide a rudimentary account of the unitary group approach to the many-electron correlation problem. They represent neither a review nor an original article, and the references are handled accordingly. In the limited space-time at our disposal, we cannot but briefly outline the basic concepts and procedures, completely avoiding any proofs or derivations.


Matrix Element Unitary Group Weight Generator Carrier Space Generator Matrix Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    M. Moshinsky, Group Theory and the Many-Body Problems (Gordon and Breach, New York, 1968); first appeared in “Many-Body Problems and Other Selected Topics in Theoretical Physics” (Lectures of the Latin American School of Physics, University of Mexico, July-August 1965 ), M. Moshinsky, T.A. Brody and G. Jacob, Eds. ( Gordon and Breach, New-York, 1966 ).Google Scholar
  2. 2.
    P. Jordan, Z. Physik 94, 531 (1935).ADSCrossRefGoogle Scholar
  3. 3.
    I.M. Gelfand and M.L. Tsetlin, Dokl. Akad. Nauk SSSR, 71, 825, 1017 (1950); I.M. Gelfand and M.I. Graev, Izv. Akad. Nauk SSSR, Ser. Mat. 29, 1329 (1965) [Amer. Math. Soc. Transl. 64, 116 (1967)]; M. Moshinsky, J. Math. Phys. 4, 1128 (1963); G.E. Baird and L.C. Biedenharn, J. Math. Phys. 1449 (1963); 5, 1723, 1730 (1964); 6, 1847 (1965); W.J. Holman, III and L.C. Biedenharn, in “Group Theory and Its Applications”, Vol. 2, E.M. Loebl, Ed. (Academic Press, New-York, 1971), p.1; J.D. Louck, Amer. J. Phys. 38, 3 (1970).Google Scholar
  4. 4.
    H. Weyl, The Classical Groups, Their Invariants and Representations (Princeton University Press, Princeton, New Jersey, 1939); The Theory of Groups in Quantum Mechanics (Dover New York, 1931); cf. also a modern account by W. Miller, Jr., Symmetry Groups and Their Applications (Academic Press, New York, 1972 ); P.P. Zelobenko, Compact Lie Groups and Their Representations (American Mathematical Society, Providence, Rhode Island, 1973 ).Google Scholar
  5. 5.
    M. Moshinsky and T.H. Seligman, Annals of Physics [N.Y.] 66, 311 (1971); T.H. Seligman, in “Second International Colloquium on Group Theoretical Methods in Physics” ( University of Nijmegen, Holland, 1973 ).Google Scholar
  6. 6.
    J. Patera, J. Chem. Phys., 56, 1400 (1972).ADSCrossRefGoogle Scholar
  7. 7.
    P.E.S. Wormer and A. van der Avoird, J. Chem. Phys. 57, 2498 (1972); Int. J. Quantum Chem. 8, 715 (1974); P.E.S. Wormer, Ph.D. Thesis, University of Nijmegen, The Netherlands, 1975.ADSCrossRefGoogle Scholar
  8. 8.
    W.G. Harter, Phys. Rev. A8, 2819 (1973); W.G. Harter and C.W. Patterson, Phys. Rev. A13, 1067 ( 1976 ); C.W. Patterson and W.G. Harter, J. Math. Phys. (to be published); Unitary Calculus I and II (Springer Lecture Notes in Physics, to be published).Google Scholar
  9. 9.
    J. Paldus, J. Chem. Phys. 6, 5321 (1974); Intern. J. Quantum Chem. £9, 165 (1975); in “Theoretical Chemistry: Advances and Perspectives”, Vol.2, H. Eyring and D.J. Henderson, Eds. ( Academic Press, New-York, 1976 ), p. 131.Google Scholar
  10. 10.
    F.A. Matsen, Intern. J. Quantum Chem. £8, 379 (1974); The Hückel-Hubbard Theory of Organic Chemistry (to be published); The Unitary Group Formulation of the Many-Body Problem, Intern. J. Quantum Chem. (to be published).Google Scholar
  11. 11.
    J.-F. Gouyet, R. Schranner and T.H. Seligman, J. Phys. A: Math. Gen. J3, 285 (1975); J.-F. Gouyet, Rev. Mex. Fis. (in print).Google Scholar
  12. 12.
    A.A. Cantu, D.J. Klein, F.A. Matsen, and T.H. Seligman, Theor. Chim. Acta 38, 341 (1975).MathSciNetCrossRefGoogle Scholar
  13. 13.
    J. Drake, G.W.F. Drake, and M. Schlesinger, J. Phys. B8, 1009 (1975).ADSGoogle Scholar
  14. 14.
    R.W. Wetmore and G.A. Segal, Chem. Phys. Letters 36, 478 (1975).ADSCrossRefGoogle Scholar
  15. 15.
    G.H.F. Diercksen, Theoret. Chim. Acta 33., 1 (1974).Google Scholar
  16. 16.
    T. Sebe and J. Nachamkin, Annals of Physics [N.Y.] 51, 100 (1969); R.R. Whitehead, Nucl. Phys. A 182, 290 (1972); R.R. Whitehead and A. Watt, Phys. Letters 41B, 7 (1972).Google Scholar
  17. 17.
    B. Roos, Chem. Phys. Letters 15, 153 (1972); in “Computational Techniques in Quantum Chemistry and Molecular Physics”, Proceedings of the NATO Advanced Study Institute at Ramsau, Germany; G.H.F. Diercksen, B.T. Sutcliffe and A. Veillard, Eds. (D. Reidel Publ. Co., Dordrecht-Holland, Boston-USA, 1975), p. 251, B. Roos and P. Siegbahn, in “Modern Theoretical Chemistry, Vol. II. Electronic Structure: Ab Initio Methods”, H.F. Schaefer, Ed. (Plenum Publishing Corp.), in print; A.H. Pakiari and N.C. Handy, Theoret. Chim. Acta 40, 17 (1975).Google Scholar
  18. 18.
    R.F. Hausman, S.D. Bloom and C.F. Bender, Chem. Phys. Letters 32, 483 (1975).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • J. Paldus
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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