Applications of unitary symmetry and combinatorics

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 un...

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Bibliographic Details
Main Author Louck, James D
Format eBook Book
LanguageEnglish
Published Singapore World Scientific Publishing Co. Pte. Ltd 2011
World Scientific
World Scientific Publishing Company
WORLD SCIENTIFIC
WSPC
Edition1
Subjects
Combinatorial analysis
Eightfold way (Nuclear physics)
Symmetry (Physics)
Unitary Symmetry
Combinatorics Binary Tree
Angular Momentum Theory
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ISBN9789814350716
9814350710
DOI10.1142/8161

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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 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 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.
ISBN:9789814350716
9814350710
DOI:10.1142/8161