Applications of unitary symmetry and combinatorics [[electronic resource] /] / James D. Louck

• Autore: Louck James D
• Pubblicazione: Hackensack, N.J., : World Scientific, c2011
• Descrizione fisica: 1 online resource (381 p.)
• Disciplina: 511.6
• Soggetto topico: Symmetry (Physics); Combinatorial analysis
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Preface and Prelude; OVERVIEW AND SYNTHESIS OF BINARY COUPLING THEORY; TOPICAL CONTENTS; MATTERS OF STYLE, READERSHIP, AND RECOGNITION; Contents; Notation; 1 Composite Quantum Systems; 1.1 Introduction; 1.2 Angular Momentum State Vectors of a Composite System; 1.2.1 Group Actions in a Composite System; 1.3 Standard Form of the Kronecker Direct Sum; 1.3.1 Reduction of Kronecker Products; 1.4 Recoupling Matrices; 1.5 Preliminary Results on Doubly Stochastic Matrices and Permutation Matrices; 1.6 Relationship between Doubly Stochastic Matrices and Density Matrices in Angular Momentum Theory ; 2 Algebra of Permutation Matrices2.1 Introduction; 2.2 Basis Sets of Permutation Matrices; 2.2.1 Summary; 3 Coordinates of A in Basis P n(e,p); 3.1 Notations; 3.2 The A-Expansion Rule in the Basis P n(e,p); 3.3 Dual Matrices in the Basis Set Σn(e, p); 3.3.1 Dual Matrices for Σ3(e, p); 3.3.2 Dual Matrices for Σ4(e, p); 3.4 The General Dual Matrices in the Basis Σn(e, p); 3.4.1 Relation between the A-Expansion and Dual Matrices; 4 Further Applications of Permutation Matrices; 4.1 Introduction; 4.2 An Algebra of Young Operators; 4.3 Matrix Schur Functions ; 4.4 Real Orthogonal Irreducible Representations of Sn4.4.1 Matrix Schur Function Real Orthogonal Irreducible Representations; 4.4.2 Jucys-Murphy Real Orthogonal Representations; 4.5 Left and Right Regular Representations of Finite Groups; 5 Doubly Stochastic Matrices in Angular Momentum Theory; 5.1 Introduction; 5.2 Abstractions and Interpretations; 5.3 Permutation Matrices as Doubly Stochastic; 5.4 The Doubly Stochastic Matrix for a Single System with Angular Momentum J; 5.4.1 Spin-1/2 System; 5.4.2 Angular Momentum-j System ; 5.5 Doubly Stochastic Matrices for Composite Angular Momentum Systems5.5.1 Pair of Spin-1/2 Systems; 5.5.2 Pair of Spin-1/2 Systems as a Composite System; 5.6 Binary Coupling of Angular Momenta; 5.6.1 Complete Sets of Commuting Hermitian Observables; 5.6.2 Domain of Definition RT (j); 5.6.3 Binary Bracketings, Shapes, and Binary Trees; 5.7 State Vectors: Uncoupled and Coupled; 5.8 General Binary Tree Couplings and Doubly Stochastic Matrices; 5.8.1 Overview; 5.8.2 Uncoupled States; 5.8.3 Generalized WCG Coefficients; 5.8.4 Binary Tree Coupled State Vectors ; 5.8.5 Racah Sum-Rule and Biedenharn-Elliott Identity as Transition Probability Amplitude Relations5.8.6 Symmetries of the 6 - j and 9 - j Coefficients; 5.8.7 General Binary Tree Shape Transformations; 5.8.8 Summary; 5.8.9 Expansion of Doubly Stochastic Matrices into Permutation Matrices; 6 Magic Squares; 6.1 Review; 6.2 Magic Squares and Addition of Angular Momenta; 6.3 Rational Generating Function of Hn(r); 7 Alternating Sign Matrices; 7.1 Introduction; 7.2 Standard Gelfand-Tsetlin Patterns; 7.2.1 A-Matrix Arrays; 7.2.2 Strict Gelfand-Tsetlin Patterns ; 7.3 Strict Gelfand-Tsetlin Patterns for λ = (n n . 1 · · · 2 1)
• Sommario/riassunto: This monograph is a synthesis of the theory of the pairwise coupling of the angular momenta of arbitrarily many independent systems to the total angular momentum in which the universal role of doubly stochastic matrices and their quantum-mechanical probabilistic interpretation is a major theme. A uniform viewpoint is presented based on the structure of binary trees. This includes a systematic method for the evaluation of all 3n-j coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrice
• Titolo autorizzato: Applications of unitary symmetry and combinatorics
• ISBN: 1-283-43383-4; 9786613433831; 981-4350-72-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910789068503321
• Lo trovi qui: Univ. Federico II