Introduction: Symmetry and the Selection of Variables |
Algebraic Elements |
Reduction Procedure and Irreducible Tensorial Sets |
Further Aspects of Reduction |
Structure of the Book |
Quaternions |
State Representatives and r -Transformations: Their Construction and Properties / Part A: |
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 3-j |
Coefficients |
Tensorial Aspects of Quantum Physics / Part B: |
Tensorial Sets of Quantum Operators |
The Liouville Representation of Quantum Mechanics |
Quantum Mechanics of Particles with Spin 1/2 |
Two-Level Systems |
Particles With Spin j >1/2: Wigner-Eckart Theorem |
Systems with 2j +1 Levels |
Transfer of Angular Momentum |
Calculation of Matrix Elements |
Recoupling Transformations: 6-j and 9-j |
Transformation Matrices and Their Analysis |
Symmetrized Recoupling: 6-j and9-j |
Products of Operators |
Combining Operators of Different Systems |
Illustrations |
Partially Filled Shells of Atoms or Nuclei |
Qualitative Discussion |
Shell-wide Treatment |
Algebra of Triple Tensors and Its Applications |
Symmetries of Higher Dimensions / Part C: |
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 |
Four-Dimensional Rotations: the Coulomb-Kepler 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 |
Introduction: Symmetry and the Selection of Variables |
Algebraic Elements |
Reduction Procedure and Irreducible Tensorial Sets |