Description 
1 online resource (xiv, 333 pages) : illustrations 
Contents 
Introduction: Symmetry and the Selection of Variables. Algebraic Elements. Reduction Procedure and Irreducible Tensorial Sets. Further Aspects of Reduction. Structure of the Book. Quaternions. Part A: State Representatives and r<$>Transformations: Their Construction and Properties. Infinitesimal Rotations and Angular Momentum:<$> Basic Relations. Analytical Example: Infinitesimal Transformation of Cartesian Coordinates. The Angular Momentum Matrices of Quantum Mechanics. The Fundamental Representation. Frame Reversal and Complex Conjugation:<$> Analytical Representation and Implications of Frame Reversal. Contragradience and the Construction of Invariants. Cartesian Base for Integer j<$> [greater than or equal to sign here]1. Standard r<$>Transformation Matrices and Their Applications:<$> Explicit Form and Properties. Macroscopic Applications. Applications to Quantum Physics. Coordinate Inversion and Parity Eigenfunctions. Reduction of Direct Products (Addition of Angular Momenta):<$> Structure and Properties of the Reducing Matrix. Reduction of r<$>Transformation Products. Irreducible Product Sets. Symmetrization of Wigner Coefficients: Invariant Triple Product and 3j<$> Coefficients. Part B: Tensorial Aspects of Quantum Physics.<$> Tensorial Sets of Quantum Operators:<$> The Liouville Representation of Quantum Mechanics. Quantum Mechanics of Particles with Spin 1/2. TwoLevel Systems. Particles With Spin j<$>>1/2: WignerEckart Theorem. Systems with 2j<$>+1 Levels. Transfer of Angular Momentum. Calculation of Matrix Elements. Recoupling Transformations: 6j<$> and 9j<$> Coefficients:<$> Transformation Matrices and Their Analysis. Symmetrized Recoupling: 6j<$> and9j<$> Coefficients. Products of Operators. Combining Operators of Different Systems. Illustrations. Partially Filled Shells of Atoms or Nuclei:<$> Qualitative Discussion. Shellwide Treatment. Algebra of Triple Tensors and Its Applications. PartC: Symmetries of Higher Dimensions.<$> Discrete Transformations of Coordinates:<$> Point Symmetry Operations and Their Groups. Characters of Group Representations and Their Applications. Symmetries of Molecules and Crystals. Rotation Groups in Higher Dimensions: Multiparticle Problems:<$> FourDimensional Rotations: the CoulombKepler Problem. Orthogonal Groups in Higher Dimensions. Further Developments. Lorentz Transformations and the Lorentz and Poincare Groups:<$> Lorentz Transformations. Generators and Representations of the Lorentz Group. The Inhomogenous Lorentz (Poincare) Group. Field Representations. Symmetries of the Scattering Continuum:<$> Symmetries of Radial Eigenfunctions. The Full Noninvariance Group of Hydrogen. Dynamics as Symmetry Transformations. Bibliography. Index 
Summary 
This text focuses on the physics of symmetries, developing symmetries and transformations through concrete physical examples and contexts rather than presenting the information axiomatically, mathematically, and abstractly. Readers are introduced gradually to advanced mathematical procedures, including the Wigner and Racah algebras and their applications to various symmetry groups. The book also includes some of the latest research on the use of noninvariance and noncompact groups in the consideration of relativistic and manyparticle problems of atoms and nuclei. This book is an updated replacement for the text Irreducible Tensorial Sets (Academic Press, 1959). Parts A and B of the present book grew out of occasional lectures in the intervening decades at the University of Chicago, where it became neccessary to update or elaborate upon certain points. Part C has been built more recently to deal with innovations and new information in the field of mathematical physics. The book as a whole develops the subject of symmetry from a physical point of view, allowing students and researchers to gain new insight on their subject. This book can be used both as a text and as a reference by students and scientists in the field. Adapts and extends the earlier Irreducible Tensor Sets (Academic Press, 1959) to classroom use Extends to multiparticle systems and relativity Includes problems in each chapter for homework assignments Embraces the latest research on noninvariance groups 
Analysis 
Quantum theory 
Bibliography 
Includes bibliographical references (pages 313316) and index 
Notes 
English 

Print version record 
Subject 
Quantum theory  Mathematics


Symmetry (Physics)  Methodology


Mathematical physics.


SCIENCE  Physics  Quantum Theory.


Mathematical physics


Quantum theory  Mathematics


Symmetry (Physics)  Methodology

Form 
Electronic book

Author 
Rau, A. R. P. (A. Ravi P.)

LC no. 
96002004 
ISBN 
9780080542171 

0080542174 

1281059021 

9781281059024 

9786611059026 

6611059024 
