Title The Racah-Wigner algebra in quantum theory / Lawrence C. Biedenharn, James D. Louck ; with a foreword by Peter A. Carruthers ; introduction by George W. Mackey

Published Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, 1984

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Description 1 online resource (lxxxviii, 534 pages) : illustrations Series Encyclopedia of mathematics and its applications ; v. 9. Section, Mathematics of physics Encyclopedia of mathematics and its applications ; v. 9. Encyclopedia of mathematics and its applications. Section, Mathematics of physics. Contents 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 Summary 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 algebraic aspects of angular momentum theory and the relationship between angular momentum theory and special topics in physics and mathematics are covered in this volume Notes Imprint and ISBN from label on title page verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley, Advanced Book Program, 1981 Publication taken over by Cambridge University Press in 1984 with a new copyright date Bibliography Includes bibliographical references and indexes Notes Print version record Subject Racah algebra. Quantum theory. Quantum Theory SCIENCE -- Energy. SCIENCE -- Mechanics -- General. SCIENCE -- Physics -- General. Quantum theory Racah algebra Quantentheorie Genre/Form Racah-Wigner-Algebra. Form Electronic book Author Louck, James D ISBN 9781461938163 1461938163 9781107340695 1107340691 9781107387188 1107387183 0521116171 9780521116176

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