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Applications of unitary symmetry and combinatorics [[electronic resource] /] / James D. Louck
| Applications of unitary symmetry and combinatorics [[electronic resource] /] / James D. Louck |
| Autore | Louck James D |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (381 p.) |
| Disciplina | 511.6 |
| Soggetto topico |
Symmetry (Physics)
Combinatorial analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-43383-4
9786613433831 981-4350-72-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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) |
| Record Nr. | UNINA-9910464499403321 |
Louck James D
|
||
| Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Applications of unitary symmetry and combinatorics [[electronic resource] /] / James D. Louck
| Applications of unitary symmetry and combinatorics [[electronic resource] /] / James D. Louck |
| Autore | Louck James D |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2011 |
| Descrizione fisica | 1 online resource (381 p.) |
| Disciplina | 511.6 |
| Soggetto topico |
Symmetry (Physics)
Combinatorial analysis |
| ISBN |
1-283-43383-4
9786613433831 981-4350-72-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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) |
| Record Nr. | UNINA-9910789068503321 |
|
Louck James D
|
||
| Hackensack, N.J., : World Scientific, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||