Cargando…
The Racah-Wigner algebra in quantum theory /
First published by Cambridge University Press in 1985, this series of Encyclopedia volumes attempts to present the factual body of all mathematics. Clarity of exposition and accessibility to the non-specialist were an important consideration in its design and language. The development of the algebra...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York, NY, USA :
Cambridge University Press,
1984.
|
| Colección: | Encyclopedia of mathematics and its applications ;
v. 9. Encyclopedia of mathematics and its applications. Section, Mathematics of physics. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half Title; Series Page; Title; Copyright; Contents; Contents of Volume 8; Editor's Statement; Foreword; Preface; Acknowledgments; Introduction; CHAPTER 1 Introduction; CHAPTER 2 Algebraic Structures Associated with Wigner and Racah Operators; 1. Introduction and Survey; 2. Notational Preliminaries; 3. Fundamental Wigner Operators; 4. Properties of Unit Tensor Operators; 5. Coupling of Unit Tensor Operators; 6. Consequences of Associativity; 7. A Characterization of Racah-Wigner Algebra; 8. Notes; 9. Appendix; Orthogonality of the Racah Invariant Operators; References
- CHAPTER 3 Null Space Properties and Structure Theorems for RW-Algebra1. The Pattern Calculus; Pattern Calculus Rules for Fundamental Operators; 1. The arrow pattern; 2. The labeled arrow pattern; 3. The pattern calculus factor; 2. Structural Results for the General [SU(2)] Wigner Operator; 3. Null Space Aspects of Wigner Coefficients; 4. The Possibility of Defining RW -Algebras for Symmetries Other Than Angular Momentum; 5. Note; 6. Appendices; A. DETERMINATION OF Pk FROM ITs CHARACTERISTIC ZEROS; B. SYMBOLIC FORMS OF THE WIGNER COEFFICIENTS; References
- CHAPTER 4 W-Algebra: An Algebra of Invariant Operators1. Introduction; 2. Wigner Operators for the Direct Product Group SU(2) XSU(2); 3. Construction of the W-Algebra; 4. Null Space Properties and Structure Theorems for W-Algebra; 5. The Matrix Boson Realization of Unit Racah Operators; 6. Notes; 7. Appendices; A. CANONICAL FORM OF THE RACAH COEFFICIENTS; B. PROOF OF THE REFLECTION SYMMETRY PROPERTY OF THE Pk; C. DETERMINATION OF Pk FROM ITS ZEROS; D. SYMBOLIC FORMS OF THE RACAH COEFFICIENTS; References; CHAPTER 5 Special Topics; TOPIC 1. FUNDAMENTAL SYMMETRY CONSIDERATIONS; Survey
- 1. The Wigner Theorem on Symmetry Transformations in Quantum Mechanics2. Proof of the Wigner Theorem; 3. Extension of the Wigner Theorem: Relation to the Fundamental Theorem of Projective Geometry; 4. Implications for Rotational Symmetry; 5. Time Reversal; 6. Time Reversal and Rotations; The Frobenius-Schur Invariant; 7. The Univalence Superselection Rule for Angular Momentum; 8. The Transformation of Eigenfunctions under Anti-unitary Operators: Core presentations; 9. Concluding Remark; 10. Notes; References; TOPIC 2. MONO POLAR HARMONICS; 1. Introduction and Survey
- 2. The Defining Physical Problem3. Reformulation of the Problem; 4. Further Discussion; 5. Notes; 6. Addendum. Minimal Coupling and Complex Line Bundles; References; TOPIC 3. A MINIMAL REALIZATION OF ANGULAR MOMENTUM STATES: THE SYMPLECTON; 1. Preliminary Remarks; 2. The Symplecton Realization of S U(2); 3. Notes; 4. Appendices; References; TOPIC 4. ALGEBRAIC ASPECTS OF PHYSICAL TENSOR OPERATORS; References; TOPIC 5. COMPLEX ANGULAR MOMENTA, REGGE TRAJECTORIES, AND REGGE POLES; 1. Physical Motivation; 2. The Regge Treatment of Nonrelativistic Potential Scattering; 3. An Illustrative Example