SYMMETRIES IN SCIENCE VII Spectrum-Generating Algebras and Dynamic Symmetries in Physics

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1 SYMMETRIES IN SCIENCE VII Spectrum-Generating Algebras and Dynamic Symmetries in Physics Edited by Bruno Gruber Southern Illinois University at Carbondale in Niigata Niigata, Japan and Takaharu Otsuka University of Tokyo Tokyo, Japan PLENUM PRESS NEW YORK AND LONDON

2 CONTENTS Introductory Remarks on the Occasion of the Puplic Lecture Given in the Niigata-Illinois Friendship Hall 1 F. lachello Symmetry: The Search for Order in the Universe 3 F. lachello U(15)D SU(6) Description of the SDG Boson Model 15 Y. Akiyama Dynarnical Symmetry Breaking and the Onset of Chaos in the Interacting Boson Model of Nuclei 2 3 Y. Alhassid Generating the Spectrum of Nonlinear Hamiltonians 3 9 LYa. Baranov and R.D. Levine Identifying Mixed-Symmetry States in the 0(6) Limit of the Proton-Neutron Interacting Boson Model: EO Decays of Beta-Vibrations B.R. Barrett and T. Otsuka Dynarnical Symmetry and String Theory 5 5 I. Bars U(7) Spectrum Generating Algebra for Rotations and Vibrations in Triatomic Molecules 7 5 R. Bijker, A.E.L. Dieperink, and A. Leviatan Algebraic Treatment of Collective Excitations in Baryon Spectroscopy 8 7 R. Bijker and A. Leviatan Can lachello's Idea of a Spectral Supersymmetry Be Extended into the Relativistic Domain? 103 A. Böhm and L.C. Biedenharn

3 q-deformed Interacting Boson Models in Nuclear and Molecular Physics 111 D. Bonatsos Low Lying Electric Dipole Excitations and the Interacting Boson Model 123 P. von Brentano, A. Zilges, N.V. Zamfir and R.-D. Herzberg Effective Charges, the Valence p-n Interaction, and the IBM 133 R.F. Casten and A. Wolf Dynamical Symmetries in Superdeformed Nuclei 141 J.A. Cizewski Dynamical Algebras and Superalgebras for Interacting Itinerant Many-Electron Systems 151 A. Danani and M. Rasetti Number and Isospin Dependence of the IBM3 Hamiltonian 179 J.P. Elliott, J.A. Evans and G.L. Long Scattering and Dynamical Symmetry 185 H. Feshbach Vibron Model Description of the Atom-Molecule Collisions 191 A. Frank, R. Lemus and R.D. Santiago An Intrinsic State with Definite Isospin for IBM J.N. Ginocchio and A. Leviatan Quantum Motion and Algebraic Generator Coordinate Method 215 AGozdz Boson and Fermion Operator Realisations of su(4) and Its Semisimple Subalgebras 223 B. Gruber and M. Ramek The Propagator Method to Solve the Fokker-Planck Equation 245 J.-Z. Gu and Y.-S. Ling Superdeformation and Interacting Boson Model 249 M, Honma and T. Otsuka Finite and Infinite Symmetry in (2+1)-Dimensional Field Theory 261 R. Jackiw and S.-Y. Pi Pre-Freezing Phenomenon in Superionic Materials 275 M. Kobayashi and F. Shimojo

4 Classical Solutions of Schroedinger Equations and Nonstandard Analysis 28 7 Ts. Kobayashi Atomic Supersymmetry, Oscillators, and the Penning Trap 295 V.A. Kostelecky Dynamical Symmetries in the sdg Interacting Boson Model 307 V.K.B. Kota and Y.D. Devi Non-Adiabaticity, Chaos and Topological Effects on Nuclear Collective Dynamics 32 9 D. Kusnezov Microscopic Approach to IBFM Exchange Term by Using Enforced Symmetry Conditions 345 G. Kyrchev and V. Paar Algebraic Approach to Vibrational Excitations in an Anharmonic Linear Chain R. Lemus and A. Frank Quadratic Algebras in Quantum Mechanics 373 P. Letourneau and L Vinet Partial Dynamical Symmetries 383 A. Leviatan Group 0(4) in the Nuclear IBA Model 395 P.O. Lipas Symmetry and Symmetry Breaking Latent in the Uncertainty Principle 407 K. Matsuno Electron-Molecule Collision Process: Review and Perspective of Algebraic Approäches 417 A. Mengoni Dynamic Symmetry in Hadron Physics: A Mesonic Puzzle for the U(4)DSO(4) Chain 425 N.C. Mukhopadhyay and L. Zhang QCD Foundations for Hadron Regge Trajectories and for the Arima-Iachello Symmetries of Nuclei 433 Y. Ne'eman and D. Sijacki Boson-Fermion Operators for Description of Young Diagrams and Related Topics 445 M. Nomura XI

5 Hyperinflation and Self-Similarity in Quasiperiodic One-Dimensional Lattices T. Odagaki Algebraic Models: New Developments in Molecular Speclroscopy 465 S.Oss Microscopic Picture of Interacting Boson Model 477 G. Kyrchev and V. Paar A Pairing Effect in y-soft Nuclei 497 X.-W. Pan, T. Otsuka and A. Arima "Deformed U(GI(3))" from SO q {3). 511 A. Sciarrino Mean Field Approach to the Algebraic Trearment of Molecules 523 B. Shao, N.R. Walet and R.D. Amado Spectrum Generating q-algebras for Anyons 535 A.l. Solomon and J.L Birman Interacting Boson Model and 3" Nuclear States in Even-Even Nuclei 54 5 S. Szpikowski and K. Zajac Parity Doublet Levels at Superdeformation 555 K. Sugawara-Tanabe and A. Arima Coefficients of Fractional Parentage of the Boson System with Single / and F-Spin 1/2 565 H.-Z. Sun, Q.-Z. Han, and Y.-X. Liu Giant Dipole Resonances in the SU(3) SU(2) Limit of the Interacting Boson-Fermion Model 575 A. Ventura, G. Maino and L. Zuffi Coulomb Excitation of Octupole Deformed Rotors 587 A. Vitturi A Possible Way to Generalize the O-A-l Method to Non-Degenerate j Shells Z.-S. Yang, H. Qi, X.-H. Li, A. Arima and T. Otsuka Dynamical Symmetry and Chaos in Nuclear Collective Models 605 N. Yoshinaga XII

6 Anisotropicness in Lattice Gauge Theory 613 Z.-K. Zhu, S. Takeuchi and D.H. Feng Index 629 KKi