Clebsch–Gordan coefficients of SU(3) in SU(2) and SO(3) bases

DOI10.1063/1.1286768zbMath0978.81040OpenAlexW2040361870MaRDI QIDQ2738204

D. J. Rowe, C. Bahri

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1286768

zbMATH Keywords

tensor product spacecompact semi-simple Lie groupshighest weight statesoptimizing the efficient calculationvector coherent state methods

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Computational methods for problems pertaining to quantum theory (81-08) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Coherent states (81R30)

Related Items (8)

Clebsch-Gordan coefficients for U(8)⊃O(8)⊃SU(3) ⋮ The external labelling problem and Clebsch–Gordan series of semisimple Lie algebras ⋮ Algorithms for SU(n) boson realizations and D-functions ⋮ Permutation-symmetric three-particle hyper-spherical harmonics based on the \(\operatorname{S}_{3}\otimes\operatorname{SO}(3)_{rot} \subset \operatorname{O}(2)\otimes\operatorname{SO}(3)_{ rot} \subset \operatorname{U}(3) \rtimes \operatorname{S}_{2} \subset \operatorname{O}(6)\) subgroup chain ⋮ A new procedure for constructing basis vectors of irreducible representations of SU(3) under the $$ SU(3) \supset SO(3) $$ basis ⋮ Programs for generating Clebsch-Gordan coefficients of \(SU(3)\) in \(SU(2)\) and \(SO(3)\) bases ⋮ Racah’s method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases ⋮ Vector coherent state theory of the generic representations of so(5) in an so(3) basis

Cites Work

• Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations
• Simple Derivation of the Clebsch-Gordan Coefficients
• Explicit orthonormal Clebsch–Gordan coefficients of SU(3)
• Clebsch-Gordan coefficients of SU(3) with simple symmetry properties
• Vector coherent state theory and its application to the orthogonal groups
• On resolving the multiplicity of arbitrary tensor products of the U(N) groups
• Screening and vertex operators for u(n)
• Representations of the Weyl group and Wigner functions for SU(3)
• An algebraic algorithm for calculating Clebsch–Gordan coefficients; application to SU(2) and SU(3)
• Wigner and Racah coefficients for SU3
• Resolution of missing label problems; a new perspective on K-matrix theory
• Induced shift tensors in vector coherent state theory
• Wigner Coefficients for the S<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">U</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Group and some Applications
• Representations of finite U3 transformations
• General Coupling Coefficients for the Group SU(3)
• Canonical Definition of Wigner Coefficients in Un

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