Polynomial Algebras and Higher Spins

Details Polynomial Algebras and Higher Spins Polynomial Algebras and Higher Spins

1996-02-02

arxiv.org/abs/hep-th/9602008v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, LaTeX

Scientific paper

10.1016/0375-9601(96)00631-7

Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in finite dimensional Fock spaces. The connection between $su(2)$ Lie algebra and q-oscillators with a root of unity q-parameter is considered. The meaning of the polynomial relations from the point of view of quantum mechanics on a sphere are discussed.

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