LEADER 05264nam 2200649 a 450 001 9910464499403321 005 20200520144314.0 010 $a1-283-43383-4 010 $a9786613433831 010 $a981-4350-72-9 035 $a(CKB)3400000000016747 035 $a(EBL)840615 035 $a(OCoLC)858228500 035 $a(SSID)ssj0000644804 035 $a(PQKBManifestationID)12255385 035 $a(PQKBTitleCode)TC0000644804 035 $a(PQKBWorkID)10680253 035 $a(PQKB)11718938 035 $a(MiAaPQ)EBC840615 035 $a(WSP)00008161 035 $a(Au-PeEL)EBL840615 035 $a(CaPaEBR)ebr10524594 035 $a(CaONFJC)MIL343383 035 $a(EXLCZ)993400000000016747 100 $a20110823d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplications of unitary symmetry and combinatorics$b[electronic resource] /$fJames D. Louck 210 $aHackensack, N.J. $cWorld Scientific$dc2011 215 $a1 online resource (381 p.) 300 $aDescription based upon print version of record. 311 $a981-4350-71-0 320 $aIncludes bibliographical references and index. 327 $aPreface 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 327 $a2 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 ?n(e, p); 3.3.1 Dual Matrices for ?3(e, p); 3.3.2 Dual Matrices for ?4(e, p); 3.4 The General Dual Matrices in the Basis ?n(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 327 $a4.4 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 327 $a5.5 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 327 $a5.8.5 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 327 $a7.3 Strict Gelfand-Tsetlin Patterns for ? = (n n . 1 · · · 2 1) 330 $aThis 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 606 $aSymmetry (Physics) 606 $aCombinatorial analysis 608 $aElectronic books. 615 0$aSymmetry (Physics) 615 0$aCombinatorial analysis. 676 $a511.6 700 $aLouck$b James D$044887 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464499403321 996 $aApplications of unitary symmetry and combinatorics$91936004 997 $aUNINA