Polynomial Algebras and Higher Spins

Abstract

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.

8 pages, LaTeX

References in corpus (1)

• Path Integrals with Generalized Grassmann Variables

Cited by in corpus (2)

• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• Nonlinear n-Pseudo Fermions