## Abstract

We consider the "missing label" problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3) ⊃ O(3) ⊃ O(2). We prove that only two independent O(3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L^{2} and the two SU(3) Casimir operators C ^{(2)} and C^{(3)}. Any one of these two operators (of third and fourth order in the generators) can be added to C^{(2)}, C ^{(3)}, L^{2}, and L_{3} to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X^{(3)} and X^{(4)} are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.

Original language | English (US) |
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Pages (from-to) | 1787-1799 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 15 |

Issue number | 10 |

DOIs | |

State | Published - 1973 |