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This monograph integrates unitary symmetry and combinatorics, showing in great detail how the coupling of angular momenta in quantum mechanics is related to binary trees, trivalent trees, cubic graphs, MacMahon's master theorem, and other basic combinatorial concepts. A comprehensive theory of recoupling matrices for quantum angular momentum is developed. For the general unitary group, polynomial forms in many variables called matrix Schur functions have the remarkable property of giving all irreducible representations of the general unitary group and are the basic objects of study. The struct

Combinatorial analysis. --- Eightfold way (Nuclear physics) --- Unitary symmetry --- Group theory --- Particles (Nuclear physics) --- Combinatorics --- Algebra --- Mathematical analysis --- Analyse combinatoire. --- Symétrie unitaire.

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This 1985 text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature and shows how this concept relates to applied areas of research in modern quantum physics.

Angular momentum. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Moment of momentum --- Momentum, Angular --- Momentum (Mechanics)

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First published by Cambridge University Press in 1985, this series of Encyclopedia volumes attempts to present the factual body of all mathematics. Clarity of exposition and accessibility to the non-specialist were an important consideration in its design and language. The development of the algebraic aspects of angular momentum theory and the relationship between angular momentum theory and special topics in physics and mathematics are covered in this volume.

Racah algebra. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Algebra, Racah --- Angular momentum --- Matrices --- Representations of groups --- Racah algebra --- Quantum theory