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Quantization of the continuous Heisenberg ferromagnet

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Abstract

The quantization of the continuous anisotropic Heisenberg ferromagnet with uniaxial anisotropy is performed by means of the quantum inverse scattering method. The space of quantum states is shown to possess the positive metric only in the su(1, 1) case (the magnet on the hyperboloid). The requirement of complete integrability leads, in the anisotropic case, to a deformation of the algebra of observables. The problem of local integrals of motion is discussed. The Hamiltonian is constructed for two-particle states.

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  1. Leningrad Branch, Steklov Mathematical Institute, Fontanka 27, 191011, Leningrad, USSR

    E. K. Sklyanin

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  1. E. K. Sklyanin
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Sklyanin, E.K. Quantization of the continuous Heisenberg ferromagnet. Lett Math Phys 15, 357–368 (1988). https://doi.org/10.1007/BF00419595

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  • DOI: https://doi.org/10.1007/BF00419595

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