The Resource Applications of unitary symmetry and combinatorics, James D. Louck

Applications of unitary symmetry and combinatorics, James D. Louck

Label
Applications of unitary symmetry and combinatorics
Title
Applications of unitary symmetry and combinatorics
Statement of responsibility
James D. Louck
Creator
Subject
Language
eng
Cataloging source
BTCTA
http://library.link/vocab/creatorName
Louck, James D
Index
index present
LC call number
QC174.17.S9
LC item number
L68 2011
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Symmetry (Physics)
  • Combinatorial analysis
Label
Applications of unitary symmetry and combinatorics, James D. Louck
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 327-333) and index
Contents
  • Group Actions in a Composite System
  • Binary Tree Coupled State Vectors
  • 5.8.5.
  • Racah Sum-Rule and Biedenharn-Elliott Identity as Transition Probability Amplitude Relations
  • 5.8.6.
  • Symmetries of the 6 --- j and 9 --- j Coefficients
  • 5.8.7.
  • General Binary Tree Shape Transformations
  • 5.8.8.
  • Summary
  • 5.8.9.
  • 1.3.
  • 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.
  • Standard Form of the Kronecker Direct Sum
  • 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.
  • 1.3.1.
  • Strict Gelfand-Tsetlin Patterns for λ = (nn - 1 ... 21)
  • 7.3.1.
  • Symmetries
  • 7.4.
  • Sign-Reversal-Shift Invariant Polynomials
  • 7.5.
  • Requirement of Zeros
  • 7.6.
  • Incidence Matrix Formulation
  • 8.
  • Reduction of Kronecker Products
  • Heisenberg Magnetic Ring
  • 8.1.
  • Introduction
  • 8.2.
  • Matrix Elements of H in the Uncoupled and Coupled Bases
  • 8.3.
  • Exact Solution of the Heisenberg Ring Magnet for n = 2,3,4
  • 8.4.
  • Heisenberg Ring Hamiltonian: Even n
  • 8.4.1.
  • 1.4.
  • Summary of Properties of Recoupling Matrices
  • 8.4.2.
  • Maximal Angular Momentum Eigenvalues
  • 8.4.3.
  • Shapes and Paths for Coupling Schemes I and II
  • 8.4.4.
  • Determination of the Shape Transformations
  • 8.4.5.
  • Transformation Method for n = 4
  • 8.4.6.
  • Recoupling Matrices
  • General 3(2f - 1) --- j Coefficients
  • 8.4.7.
  • General 3(2f - 1) --- j Coefficients Continued
  • 8.5.
  • Heisenberg Ring Hamiltonian: Odd n
  • 8.5.1.
  • Matrix Representations of H
  • 8.5.2.
  • Matrix Elements of Rj2:j1: The 6f --- j Coefficients
  • 8.5.3.
  • 1.5.
  • Matrix Elements of Rj3:j1: The 3(f + 1) --- j Coefficients
  • 8.5.4.
  • Properties of Normal Matrices
  • 8.6.
  • Recount, Synthesis, and Critique
  • 8.7.
  • Action of the Cyclic Group
  • 8.7.1.
  • Representations of the Cyclic Group
  • 8.7.2.
  • Preliminary Results on Doubly Stochastic Matrices and Permutation Matrices
  • Action of the Cyclic Group on Coupled State Vectors
  • 8.8.
  • Concluding Remarks
  • A.
  • Counting Formulas for Compositions and Partitions
  • A.1.
  • Compositions
  • A.2.
  • Partitions
  • B.
  • 1.6.
  • No Single Coupling Scheme for n [≥ ] 5
  • B.1.
  • No Single Coupling Scheme Diagonalizing H for n [≥ ] 5
  • C.
  • Generalization of Binary Coupling Schemes
  • C.1.
  • Generalized Systems
  • C.2.
  • Composite U(n) System Problem
  • Machine generated contents note:
  • Relationship between Doubly Stochastic Matrices and Density Matrices in Angular Momentum Theory
  • 2.
  • Algebra of Permutation Matrices
  • 2.1.
  • Introduction
  • 2.2.
  • Basis Sets of Permutation Matrices
  • 2.2.1.
  • Summary
  • 3.
  • 1.
  • Coordinates of A in Basis PΣn(e, p)
  • 3.1.
  • Notations
  • 3.2.
  • A-Expansion Rule in the Basis PΣn(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.
  • Composite Quantum Systems
  • Dual Matrices for Σ4(e, p)
  • 3.4.
  • 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.
  • 1.1.
  • Algebra of Young Operators
  • 4.3.
  • Matrix Schur Functions
  • 4.4.
  • Real Orthogonal Irreducible Representations of Sn
  • 4.4.1.
  • Matrix Schur Function Real Orthogonal Irreducible Representations
  • 4.4.2.
  • Jucys-Murphy Real Orthogonal Representations
  • 4.5.
  • Introduction
  • 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.
  • 1.2.
  • 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 Systems
  • 5.5.1.
  • Pair of Spin-1/2 Systems
  • 5.5.2.
  • Angular Momentum State Vectors of a Composite System
  • 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.
  • 1.2.1.
  • 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.
Dimensions
26 cm.
Extent
xxxv, 344 p.
Isbn
9789814350716
System control number
  • (CaMWU)u2513255-01umb_inst
  • 2519418
  • (Sirsi) i9789814350716
  • (OCoLC)707966875
Label
Applications of unitary symmetry and combinatorics, James D. Louck
Publication
Bibliography note
Includes bibliographical references (p. 327-333) and index
Contents
  • Group Actions in a Composite System
  • Binary Tree Coupled State Vectors
  • 5.8.5.
  • Racah Sum-Rule and Biedenharn-Elliott Identity as Transition Probability Amplitude Relations
  • 5.8.6.
  • Symmetries of the 6 --- j and 9 --- j Coefficients
  • 5.8.7.
  • General Binary Tree Shape Transformations
  • 5.8.8.
  • Summary
  • 5.8.9.
  • 1.3.
  • 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.
  • Standard Form of the Kronecker Direct Sum
  • 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.
  • 1.3.1.
  • Strict Gelfand-Tsetlin Patterns for λ = (nn - 1 ... 21)
  • 7.3.1.
  • Symmetries
  • 7.4.
  • Sign-Reversal-Shift Invariant Polynomials
  • 7.5.
  • Requirement of Zeros
  • 7.6.
  • Incidence Matrix Formulation
  • 8.
  • Reduction of Kronecker Products
  • Heisenberg Magnetic Ring
  • 8.1.
  • Introduction
  • 8.2.
  • Matrix Elements of H in the Uncoupled and Coupled Bases
  • 8.3.
  • Exact Solution of the Heisenberg Ring Magnet for n = 2,3,4
  • 8.4.
  • Heisenberg Ring Hamiltonian: Even n
  • 8.4.1.
  • 1.4.
  • Summary of Properties of Recoupling Matrices
  • 8.4.2.
  • Maximal Angular Momentum Eigenvalues
  • 8.4.3.
  • Shapes and Paths for Coupling Schemes I and II
  • 8.4.4.
  • Determination of the Shape Transformations
  • 8.4.5.
  • Transformation Method for n = 4
  • 8.4.6.
  • Recoupling Matrices
  • General 3(2f - 1) --- j Coefficients
  • 8.4.7.
  • General 3(2f - 1) --- j Coefficients Continued
  • 8.5.
  • Heisenberg Ring Hamiltonian: Odd n
  • 8.5.1.
  • Matrix Representations of H
  • 8.5.2.
  • Matrix Elements of Rj2:j1: The 6f --- j Coefficients
  • 8.5.3.
  • 1.5.
  • Matrix Elements of Rj3:j1: The 3(f + 1) --- j Coefficients
  • 8.5.4.
  • Properties of Normal Matrices
  • 8.6.
  • Recount, Synthesis, and Critique
  • 8.7.
  • Action of the Cyclic Group
  • 8.7.1.
  • Representations of the Cyclic Group
  • 8.7.2.
  • Preliminary Results on Doubly Stochastic Matrices and Permutation Matrices
  • Action of the Cyclic Group on Coupled State Vectors
  • 8.8.
  • Concluding Remarks
  • A.
  • Counting Formulas for Compositions and Partitions
  • A.1.
  • Compositions
  • A.2.
  • Partitions
  • B.
  • 1.6.
  • No Single Coupling Scheme for n [≥ ] 5
  • B.1.
  • No Single Coupling Scheme Diagonalizing H for n [≥ ] 5
  • C.
  • Generalization of Binary Coupling Schemes
  • C.1.
  • Generalized Systems
  • C.2.
  • Composite U(n) System Problem
  • Machine generated contents note:
  • Relationship between Doubly Stochastic Matrices and Density Matrices in Angular Momentum Theory
  • 2.
  • Algebra of Permutation Matrices
  • 2.1.
  • Introduction
  • 2.2.
  • Basis Sets of Permutation Matrices
  • 2.2.1.
  • Summary
  • 3.
  • 1.
  • Coordinates of A in Basis PΣn(e, p)
  • 3.1.
  • Notations
  • 3.2.
  • A-Expansion Rule in the Basis PΣn(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.
  • Composite Quantum Systems
  • Dual Matrices for Σ4(e, p)
  • 3.4.
  • 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.
  • 1.1.
  • Algebra of Young Operators
  • 4.3.
  • Matrix Schur Functions
  • 4.4.
  • Real Orthogonal Irreducible Representations of Sn
  • 4.4.1.
  • Matrix Schur Function Real Orthogonal Irreducible Representations
  • 4.4.2.
  • Jucys-Murphy Real Orthogonal Representations
  • 4.5.
  • Introduction
  • 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.
  • 1.2.
  • 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 Systems
  • 5.5.1.
  • Pair of Spin-1/2 Systems
  • 5.5.2.
  • Angular Momentum State Vectors of a Composite System
  • 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.
  • 1.2.1.
  • 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.
Dimensions
26 cm.
Extent
xxxv, 344 p.
Isbn
9789814350716
System control number
  • (CaMWU)u2513255-01umb_inst
  • 2519418
  • (Sirsi) i9789814350716
  • (OCoLC)707966875

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