Title: The current algebra representations of quantum many-particle Schrödinger type Hamiltonian models, their factorized structure and integrability
Author(s):

	D. Prorok (Department of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland) ,
	A.K. Prykarpatski (Institute of Mathematics, Department of Physics, Mathematics and Computer Science, Cracow University of Technology, Krakow 31-155, Poland)

There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in case of quantum integrable spatially many- and one-dimensional dynamical systems. As examples, we have studied in detail the factorized structure of Hamiltonian operators, describing such quantum integrable spatially many- and one-dimensional models as generalized oscillatory, Calogero-Sutherland, Coulomb type and nonlinear Schrödinger dynamical systems of spinless bose-particles.

Key words: Fock space, current algebra representations, Hamiltonian reconstruction, Bogolubov generating functional, Calogero-Moser-Sutherlan model, quantum integrability, quantum symmetries
PACS: 11.10.Ef, 11.15.Kc, 11.10.-z, 11.15.-q, 11.10.Wx, 05.30.-d

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