Complete sets of commuting operators and O(3) scalars in the enveloping algebra of SU(3)

B. R. Judd, Willard Miller, J. Patera, P. Winternitz

Research output: Contribution to journalArticle

97 Citations (Scopus)

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 L2 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), L2, and L3 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 languageEnglish (US)
Pages (from-to)1787-1799
Number of pages13
JournalJournal of Mathematical Physics
Volume15
Issue number10
DOIs
StatePublished - Jan 1 1973

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Enveloping Algebra
algebra
Scalar
scalars
operators
Fourth Order
Operator
Semisimple Groups
subgroups
Semisimple
Angular Momentum
Resolve
eigenvalues
generators
angular momentum
Subgroup
Generator
Eigenvalue

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Complete sets of commuting operators and O(3) scalars in the enveloping algebra of SU(3). / Judd, B. R.; Miller, Willard; Patera, J.; Winternitz, P.

In: Journal of Mathematical Physics, Vol. 15, No. 10, 01.01.1973, p. 1787-1799.

Research output: Contribution to journalArticle

Judd, B. R. ; Miller, Willard ; Patera, J. ; Winternitz, P. / Complete sets of commuting operators and O(3) scalars in the enveloping algebra of SU(3). In: Journal of Mathematical Physics. 1973 ; Vol. 15, No. 10. pp. 1787-1799.
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