A J Bracken and J H MacGibbon 1984 J. Phys. A: Math. Gen. 17 2581 doi:10.1088/0305-4470/17/13/011
A J Bracken and J H MacGibbon
Show affiliationsCreation and annihilation operators are defined which are Wigner operators (tensor shift operators) for SU(3). While the annihilation operators are simply boson operators, the creation operators are cubic polynomials in boson operators. Together they generate under commutation the Lie algebra of SO(6,2). The vector space generated from a vacuum vector by repeated application of the creation operators carries an irreducible representation of the SO(6,2) algebra, equivalent to an hermitian representation, and also carries in direct sum every different irreducible representation of SU(3)<SO(6,2) exactly once. A model for SU(3), in the sense of Bernstein, Gel'fand and Gel'fand, is therefore defined. The different SU(3) irreducible representations appear explicitly as manifestly covariant, irreducible tensors, whose orthogonality and normalisation properties are examined. Other Wigner operators for SU(3) can be constructed simply as products of the new creation and annihilation operators, or sums of such products.
02.20.Qs General properties, structure, and representation of Lie groups
20Cxx Representation theory of groups (See also 19A22 (for representation rings and Burnside rings))
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
Issue 13 (11 September 1984)
A J Bracken and J H MacGibbon 1984 J. Phys. A: Math. Gen. 17 2581
P G Grove and A C Ottewill 1983 J. Phys. A: Math. Gen. 16 3905
R J Baxter 1980 J. Phys. A: Math. Gen. 13 L61
M A Lohe 1977 J. Phys. A: Math. Gen. 10 525
J S Dowker 1977 J. Phys. A: Math. Gen. 10 115
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N. Perra et al 2009 EPL 88 48002
W. T. Cruz et al 2009 EPL 88 41001