SU(3) Clebsch-Gordan coefficients and some of their symmetries

We discuss the construction and symmetries of Clebsch-Gordan coefficients arising from basis states constructed as triple tensor products of two-dimensional harmonic oscillator states. Because of the symmetry of the basis states, matrix elements and recursion relations are easily expressed in terms...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 53; no. 2; pp. 25201 - 25233
Main Authors Martins, Alex Clésio Nunes, Suffak, Mark W, de Guise, Hubert
Format Journal Article
LanguageEnglish
Published IOP Publishing 17.01.2020
Subjects
Clebsch-Gordan coefficients
reflections
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Summary:We discuss the construction and symmetries of Clebsch-Gordan coefficients arising from basis states constructed as triple tensor products of two-dimensional harmonic oscillator states. Because of the symmetry of the basis states, matrix elements and recursion relations are easily expressed in terms of technology. As the Weyl group has a particularly simple action on these states, Weyl symmetries of the coupling coefficients generalizing the well known symmetry of coupling can be obtained, so that any coefficient can be obtained as a sum of Weyl-reflected coefficients lying in the dominant Weyl sector. Some important cases of multiplicity-free decompositions are discussed as examples of applications.
Bibliography:JPhysA-111885.R2
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab4b70