The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

Details The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

2002-04-20

arxiv.org/abs/quant-ph/0204119v1

J.Math.Phys. 43 (2002) 5262-5277

Physics

Quantum Physics

Latex, 25 pages

Scientific paper

10.1063/1.1508810

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).

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