Applications of unitary symmetry and combinatorics
 Responsibility
 James D. Louck.
 Language
 English.
 Imprint
 Singapore ; Hackensack, NJ : World Scientific, c2011.
 Physical description
 xxxv, 344 p. : ill. ; 26 cm.
Access
Available online
 ebooks.worldscinet.com World Scientific
 ebrary
Math & Statistics Library

Stacks

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QA167 .L67 2011

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QA167 .L67 2011
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Creators/Contributors
 Author/Creator
 Louck, James D.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 327333) and index.
 Contents

 Composite Quantum Systems Algebra of Permutation Matrices Coordinates of A in a Basis Applications of Permutation Matrices Doubly Stochastic Matrices in AMT Magic Squares Alternating Sign Matrices The Heisenberg Magnetic Ring.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 quantummechanical 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 3nj coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrices, the properties of magic squares and an associated generalized Regge form, the Zeilberger counting formula for alternating sign matrices, and the Heisenberg ring problem, viewed as a composite system in which the total angular momentum is conserved. The readership is intended to be advanced graduate students and researchers interested in learning about the relationship between unitary symmetry and combinatorics and challenging unsolved problems. The many examples serve partially as exercises, but this monograph is not a textbook. It is hoped that the topics presented promote further and more rigorous developments that lead to a deeper understanding of the angular momentum properties of complex systems viewed as composite wholes.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2011
 ISBN
 9789814350716 (hbk.)
 9814350710 (hbk.)