Schwinger’s oscillator realization of an SO(9) tensor operator
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The weights and representation matrices of the vector and the spinor representation of the Lie algebra SO(9) are introduced in the quantum mechanical language. Tensor product decompositions of any two of them are explicitly shown by using an algebraic method of quantum mechanics. Similar decompositions are finally achieved for a coupled tensor operator in the picture of Schwinger’s bosonic oscillators.
PACS:02.20.Qs 03.65.Fd 04.65.+e 12.60.Jv
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