SYMMETRIES IN SCIENCE II

Transcription

1 SYMMETRIES IN SCIENCE II Edited by Bruno Gruber and Romuald Lenczewski Southern Illinois University Carbondale, Illinois PLENUM PRESS NEW YORK AND LONDON

2 CONTENTS The Mysterious World of Symmetry in Physics 1 F. Iachello De Sitter Structured Connection and Gauge Translations R.R. Aldinger The Algebraic Approach to Scattering and the "Euclidean Connection" 29 Y. Alhassid Symmetry and Dynamics. Two Distinct Methodologies from Kepler to Supersymmetry 37 A.O. Barut Topological Concepts in Nuclear Physics: The Deuteron as a Bl-Skyrmion 51 L.C. Biedenharn, E. Sorace, and M. Tarlini QCD and Nuclear Structure 51 K. Bleuler Quantum Mechanics and Spectrum Generating Groups and Supergroups 71 A. Böhm Symmetries in Heavy Nuclei and the Proton-Neutron Interaction 87 R.F. Casten Time Symmetry and the Theory of Measurement 107 K. Datta Symmetry and Topology of the Configuration Space and Quantization H.D. Doebner and J. Tolar Algebraic Realization of the Rotor J.P. Draayer and Y. Leschber Special Functions and Representations of su(2) P. Feinsilver The FDS (Fermion Dynamical Symmetry) Model, Nuclear Shell Model and Collective Nuclear Structure Physics D.H. Feng ^15 ^27 -^g ^55

3 Dynamical Supersymmetric Dirac Hamiltonians 175 J.N. Ginocchio Finite Dimensional Indecomposable Representatlons of the Poincare Algebra 185 B. Gruber and R. Lenczewskl On the Behaviour of Solutions of the Laplace- Beltrami Equations A.M. Grundland Algebraic Structures of Degenerate Systems, Physlcal Requirements and the Indefinite Metrie 217 H. Gründling and C.A. Hurst Broken Symmetry and the Accelerated Observer 225 CT. Hill Quantum Theory of the Free Electromagnetic Field 235 C.A. Hurst Dynamic Symmetries in Scattering 247 F. Iachello Factorization-Algebraization-Path Integration and Dynamical Groups 255 A. Inomata and R. Wilson Classification of Operators in Atomic Spectroscopy by Lie Groups 265 B.R. Judd An Introduction to Squeezed States 271 J.R. Klauder On Geometry of Phenomenological Thermodynamics 279 J. Kocik On Protections of Spinor Spaces onto Minkowski Space 289 J. Kocik and J. Rzewuski s.d.g. IBM and the Embedding Method 313 Y. Ling, S. Dong, and D. Ji Are the Dirac Strings Harmless? 323 H.J. Lipkin and M. Peshkin Physical Models on Discrete Space and Time 329 M. Lorente The Many Symmetries of Hubbard Alternant Polyenes 343 F.A. Matsen Symmetries and Polarization 355 M.J. Moravcsik Boson Realization of Symplectic Algebras and the Matrix Representation of Their Generators 361 M. Moshinsky

4 Integral Transforms on Homogeneous Spaces of the De Sitter and Conformal Groups 367 P. Moylan Vector-Scalar Version of the Dirac Lagrangian 375 P.L. Nash Double Covering of Diffeomorphisms for Superstrings in Generic Curved Space 381 Y. Ne eman and D. Sijacki Systems, Subsystems and Induced Representations 393 D.J. Newman Symmetry Between Bosons and Fermions 407 Y. Ohnuki and S. Kamefuchi General Dynkin Indices and Their Applications 419 S. Okubo Group Theoretical Approaches to Many-Electron Correlation Problem 429 J. Paldus On the Representations of the Basic Lie Superalgebras: Gel'fand Zetlin Basis for sl(l,n) 447 T.D. Palev The Use of Symmetry in Molecular Ab-Initio SCF Calculations M. Ramek "Clifford Algebraic Symmetries in Physics" 467 N. Salingaros Squeezed States and Quadratic Hamiltonians: A Wigner Distribution Approach 471 R. S imon Light and Group Theory 483 E.C.G. Sudarshan Symmetry-Adaptation and Selection Rules for Effective Crystal Field Hamiltonians 493 J.A. Tuszyhski Symmetry-Breaking in Biological Cells 503 J.A. Tuszynski A Non-Equilibrium Theory for Phase Transitions and the Expanding Universe 517 H. Umezawa Symmetries and Special Functions 531 N.Ya. Vilenkin and A.U. Klimyk Observable Manifestations of Invariance in Condensed Matter and Biological Systems 547 G. Vitiello

5 Relativistic Scattering of Composite Particles 555 R. Wilson Empirical Evidences for Fermion Dynamical Symmetries in Nuclei 567 C.-L. Wu S0(2. + 1) D? 3 SO (3) in Group Chains for L-S Coupling. 585 Z.Y. Wu, C.P. Sun, L. Zhang, and B.F. Li The Supersymmetry of the Dirac-Yang-Mills Operator and Some Applications 591 L. O'Raifeartaigh Index 601