Unitary Group Approach to the Many-Electron Correlation Problem

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.

[1]  P. Wormer,et al.  Calculation of permutation matrices using graphical methods of spin algebras: Explicit expressions for the Serber-coupling case , 1978 .

[2]  H. Weyl.  The Classical Groups , 1940 .

[3]  A. Barut,et al.  Theory of group representations and applications , 1977 .

[4]  P. Phariseau,et al.  Electrons in Finite and Infinite Structures , 1977 .

[5]  Projected basis set for the irreducible representation {2N/2−S,12S}ofU(n) , 1978 .

[6]  A second quantized formulation of valence bond theory , 1975 .

[7]  G. B. Robinson,et al.  Representation theory of the symmetric group , 1961 .

[8]  J. Patera.  Electron g3 Configurations in LS Coupling , 1972 .

[9]  Geerd H. F. Diercksen,et al.  Optimized transformation of four center integrals , 1974 .

[10]  T. Seligman,et al.  Spin recoupling and n-electron matrix elements , 1975 .

[11]  Josef Paldus,et al.  Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems , 1974 .

[12]  G. Segal,et al.  Efficient generation of configuration interaction matrix elements , 1975 .

[13]  Geerd H. F. Diercksen,et al.  Computational techniques in quantum chemistry and molecular physics : proceedings of the NATO Advanced Study Institute held at Ramsau, Germany, 4-21 September, 1974 , 1975 .

[14]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[15]  Frederick A. Matsen.  Spin-Free quantum chemistry. XVIII. The unitary group formulation of the many-electron problem† , 1976 .

[16]  Josef Paldus,et al.  Unitary-group approach to the many-electron correlation problem: Relation of Gelfand and Weyl tableau formulations , 1976 .

[17]  J. Mulder.  On the number of configurations in an N-electron system , 1966 .

[18]  T. Seligman,et al.  Group theory and second quantization for nonorthogonal orbitals , 1971 .

[19]  Josef Paldus,et al.  Time-Independent Diagrammatic Approach to Perturbation Theory of Fermion Systems , 1975 .

[20]  M. Moshinsky.  Group Theory and the Many Body Problem , 1968 .

[21]  J. Cizek,et al.  An algebraic approach to bound states of simple one‐electron systems , 1977 .

[22]  A. J. Coleman.  Induced and Subduced Representations , 1968 .

[23]  Josef Paldus,et al.  Correlation problems in atomic and molecular systems. V. Spin‐adapted coupled cluster many‐electron theory , 1977 .

[24]  P. Wormer,et al.  Transformation properties of antisymmetric spin eigenfunctions under linear mixing of the orbitals , 1972 .

[25]  I. Morrison,et al.  Computational Methods for Shell Model Calculations , 1977 .

[26]  R. R. Whitehead,et al.  A numerical approach to nuclear shell-model calculations , 1972 .

[27]  P. Jordan.  Der Zusammenhang der symmetrischen und linearen Gruppen und das Mehrkörperproblem , 1935 .

[28]  W. Harter.  Alternative Basis for the Theory of Complex Spectra , 1973 .

[29]  Michael A. Robb,et al.  The computation of the representation matrices of the generators of the unitary group , 1977 .

[30]  H. Weyl.  The Theory Of Groups And Quantum Mechanics , 1931 .

[31]  Per E. M. Siegbahn,et al.  The Direct Configuration Interaction Method from Molecular Integrals , 1977 .

[32]  H. Weyl.  Gruppentheorie und Quantenmechanik , 1928 .

[33]  Frederick Albert Matsen IV,et al.  The Unitary Group and the Many-Body Problem , 1978 .

[34]  F. Sasaki.  Matrix elements in configuration interaction calculations , 1974 .

[35]  On the representation matrices of the spin permutation group , 1977 .

[36]  J. D. Louck,et al.  Recent Progress Toward a Theory of Tensor Operators in the Unitary Groups , 1970 .

[37]  A. Bohm,et al.  Dynamical Groups and Spectrum Generating Algebras , 1971 .

[38]  J. Humphreys.  Introduction to Lie Algebras and Representation Theory , 1973 .

[39]  H. Schaefer.  Methods of Electronic Structure Theory , 1977 .

[40]  T. Sebe,et al.  Variational buildup of nuclear shell model bases , 1969 .

[41]  C. W. Patterson,et al.  A Unitary Calculus for Electronic Orbitals , 1976 .

[42]  Isaiah Shavitt,et al.  The Method of Configuration Interaction , 1977 .

[43]  F. A. Matsen,et al.  Spin-Free Quantum Chemistry , 1964 .

[44]  B. G. Adams,et al.  Application of graphical methods of spin algebras to limited CI approaches. I. Closed shell case , 1977 .

[45]  T. Gaisser,et al.  Hadronic Production of Narrow Vector Mesons , 1977 .

[46]  Mordechay Schlesinger,et al.  Vector-coupling approach to orbital and spin-dependent tableau matrix elements in the theory of complex spectra , 1977 .

[47]  R. F. Hausman,et al.  A new technique for describing the electronic states of atoms and molecules — The vector method☆ , 1975 .

[48]  小谷 正雄.  Tables of molecular integrals , 1955 .

[49]  Douglas Rayner Hartree,et al.  On the Intensity of Total Scattering of X-Rays , 1929 .

[50]  Ernest M. Loebl,et al.  Group theory and its applications , 1968 .

[51]  L. Biedenharn,et al.  On the Representations of the Semisimple Lie Groups. II , 1963 .

[52]  A. Watt,et al.  Shell-Model and protected Hartree-Fock calculations for 24Mg, 28Si and 32S , 1972 .

[53]  A. Mullin,et al.  Group Theory and its Applications to Physical Problems , 1962 .

[54]  秋山 佳巳.  E. El Baz and B. Castel: Graphical Methods of Spin Algebras in Atomic, Nuclear, and Particle Physics, Marcel Dekker, New York 1972, x+428 ページ, 23.5×16cm, 7,020円 , 1973 .

[55]  D. Faddeev,et al.  Computational Methods of Linear Algebra , 1959 .