A pair of commuting scalars for G(2) ⊇ SU(2)×SU(2)

G(2) ⊇ SU(2)×SU(2) is a two‐missing‐labels problem, and therefore in order to give a complete and orthogonal specification of states of irreducible representations of G(2) in an SU(2)×SU(2) basis, one needs to find a pair of commuting Hermitian operators which are scalar with respect to the SU(2)×SU...

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Veröffentlicht in:Journal of mathematical physics 1985-05, Vol.26 (5), p.894-900
Hauptverfasser: Hughes, J. W. B., Van der Jeugt, J.
Format: Artikel
Sprache:eng
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Zusammenfassung:G(2) ⊇ SU(2)×SU(2) is a two‐missing‐labels problem, and therefore in order to give a complete and orthogonal specification of states of irreducible representations of G(2) in an SU(2)×SU(2) basis, one needs to find a pair of commuting Hermitian operators which are scalar with respect to the SU(2)×SU(2) subalgebra. A theorem due to Peccia and Sharp states that there are, apart from the Lie algebra invariants, twice as many functionally independent scalars as missing labels. Here two commuting SU(2)×SU(2) scalars are obtained, both of sixth order in the G(2) basis elements. They are in fact combinations of five scalars of different tensorial types, indicating that the functionally independent ones are in general insufficient to provide the lowest‐order commuting scalars. An expression for the sixth‐order invariant of G(2) is also obtained.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.526545