Nonscalar extension of shift operator techniques for SU (3) in an O(3) basis. I. Theory

DOI10.1063/1.524817zbMath0495.22015OpenAlexW2124744279MaRDI QIDQ3958684

J. W. B. Hughes, H. E. De Meyer, Guido Vanden Berghe

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1063/1.524817

zbMATH Keywords

eigenvaluesreductionsymmetry reductionSU(3)O(3)degeneracy labelling

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Compact groups (22C05)

Related Items (9)

On the spectra of SO(3) scalars in the enveloping algebra of SU(3) ⋮ A pair of commuting scalars for G(2) ⊇ SU(2)×SU(2) ⋮ The shift operator technique for SO(7) in an [SU(2)3 basis. I. Theory] ⋮ SU(2)×SU(2) shift operators and representations of SO(5) ⋮ A general approach to the systematic derivation of SO(3) shift operator relations. II. Applications ⋮ Totally symmetric irreducible representations of the group SO(6) in the principal SO(3) subgroup basis ⋮ Nonscalar extension of shift operator techniques for SU(3) in an O(3) basis. III. Shift operators of second degree in the tensor components ⋮ Shift operator approach of the spin-isospin supermultiplet state labelling problem: Eigenvalue determination of the \(\Omega\) and \(\Phi\) labelling operators ⋮ Nonscalar extension of shift operator techniques for SU (3) in an O(3) basis. II. Applications

Cites Work

• Everything you always wanted to know about \(SU(3)\subset 0(3)\)
• O(3) shift operators: The general analysis
• Sum rules for the matrices of the generators of SU(3) in an SO(3) basis
• Shift operator techniques for the classification of multipole-phonon states. VI. Properties of nonscalar R(3) product operators in the R(2λ+1) groups
• Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)

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