Group Theoretical Methods in Physics

Group Theoretical Methods in Physics

1st Edition - January 1, 1977
  • Editor: Robert Shar
  • eBook ISBN: 9780323141529

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Description

Group Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics. This book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic symmetry. Organized into six parts encompassing 64 chapters, this book begins with an overview of the theories of nuclear quadrupole dynamics. This text then examines the conventional approach in the determination of superstructures. Other chapters consider the Hamiltonian formalism and how it is applied to the KdV equation and to a slight variant of the KdV equation. This book discusses as well the significant differential equations of mathematical physics that are integrable Hamiltonian systems, including the equations governing self-induced transparency and the motion of particles under an inverse square potential. The final chapter deals with the decomposition of the tensor product of two irreducible representations of the symmetric group into a direct sum of irreducible representations. This book is a valuable resource for physicists.

Table of Contents


  • Contributors

    Preface

    Part I. Nuclei, Atoms, Solids

    Canonical Transformations and Spectrum Generating Algebras in the Theory of Nuclear Collective Motion

    Modulated Space Groups

    Properties of Lattices Associated with a Modulated Crystal

    A Hamiltonian Approach to the KdV and Other Equations

    Use of an Elementary Group Theoretical Method in Determining the Structure of a Biological Crystal from Its Patterson Function

    Invariants Polynomiaux des Groupes de Symétrie Moléculaire et Cristollographique

    Metacrystallographic Groups

    The SP(3, IR) Model of Nuclear Collective Motion

    A Group Theoretic Description of the Magnetic Phase Transitions in the AB2O4-Type Spinels

    Applications of Crystal Clebsch-Gordan Coefficients

    On the Use of the SO(4,2) Dynamical Group for the Study of the Ground State of a Hydrogen Atom in a Homogeneous Magnetic Field

    Group Theory Around Ligand Field Theory

    Finite Representations of the Unitary Group and Their Applications in Many-Body Physics

    Algebraic and Geometric Methods of Quantisation of the Isotropic Harmonic Oscillator

    The Ising Algebra

    The Group O(3)Λ(T2xT2) and the Hydrogen Atom

    Part II. Coherent States, Supersymmetry, Gauge Fields, Relativity

    Spontaneous Breaking of Exceptional Groups

    Complex Space-Times with Null Strings

    Intelligent Spin States and Heisenberg Equality

    Some Aspects of Graded Lie Algebras

    U(n,n) and Generalized Twistors

    Some Comments on Symplectic Structures in Complex Riemannian Geometry

    Coherent States on the Conformal Group and Position Operator

    Gauge Theory of the Conformal Group

    Theory of Coherent Quarks. On the Dynamical Origin of the Okubo-Zweig-Iizuka Rule

    Relativistic Coherent-State Representations

    Gauge Fields Over the Super-Symmetry Space

    On Supersymmetry and the Hope for a Non-Trivial Fusion between Internal and Space-Time Symmetries

    Physics and Lie Pseudogroups

    Part III. Classical and Quantum Mechanics

    Classical Functions Associated with Some Groups of Automorphisms of the Weyl Group

    Cyclic Groups and Adaptation in the Visual System of the Cat

    Geometrical Mechanics and Dirac Bracket

    Other Symmetries and Constants of the Motion

    Q-Symmetries and Equivalent Lagrangians

    Kinematical Symmetries of the Navier-Stokes Equation

    Normal Modes of Nonlinear Discrete Symmetric Systems by Group Representation Theory

    Part IV. Relativistic Quantum Physics

    The Concept of a Kinematical Stability Group in Implementing Relativistic Symmetry

    Causality and Symmetry in Cosmology and the Conformal Group

    Thomas-Bargmann-Michel-Telegdi Equation for Wigner Particles

    Générateurs du Groupe de Poincaré Associés aux Représentations Irréductibles Unitaires du Genre Espace

    On the Structure of 4-Vector Operators, with an Application to the Point Form of Relativistic Dynamics

    On the Localizability of Massless Particles

    On the Existence of Charges and Mass-Splitting in Relativistic Quantum Field Theory

    Particles, Mass Spectra, and Interference in Relativistic Quantum Theory

    SU(4) Breaking and the New Particles: Some Applications

    On a Group Theoretic Treatment of the Number Operator of Particles

    Poincaré Group and Magnetic Charge

    Part V. Mathematical Physics

    Solvability Questions for Invariant Differential Operators

    Symmetry and Separation of Variables for Linear Partial Differential and Hamilton-Jacobi Equations

    Subgroups of Lie Groups and Symmetry Breaking

    Conformal Harmonic Analysis and Intertwining Differential Operators

    Group Theoretic Aspects of Conservation Laws of Nonlinear Time Evolution Equations: The KdV Equation and the Cubic Schrödinger Equation

    Application of Group Theoretic Methods in Bifurcation Theory

    Harmonic Analysis on Double Classes

    Part VI. Representation Theory

    Induced Projective Representations

    Une Identité du Binôme et les Représentations Linéaires Finies de Mp(K) et GL(p,K)

    Double Classes: A New Classification Scheme for Group Elements

    A Characterization of the Standard Polynomial of Even Degree

    A Generalization of the "Associative" Property of the Killing Form

    Highest Weights of Semisimple Lie Algebras

    Projective Irreducible Unitary Representations of the Schrödinger Group with a Nontrivial Factor

    Representation of the Racah Coefficient as a Generalized Hypergeometric Function

    Polynômes Invariants d'un Certain Groupe de Transformations Lineaires

    The Clebsch-Gordan Decomposition and the Coefficients for the Symmetric Group

Product details

  • No. of pages: 684
  • Language: English
  • Copyright: © Academic Press 1977
  • Published: January 1, 1977
  • Imprint: Academic Press
  • eBook ISBN: 9780323141529

About the Editor

Robert Shar