Group Theoretical Methods in Physics

by Robert Shar (Editor)

Overview

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.

Product Details

ISBN-13:	9780323141529
Publisher:	Elsevier Science
Publication date:	12/02/2012
Sold by:	Barnes & Noble
Format:	eBook
Pages:	684
File size:	10 MB

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)?(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