Abstract
In this work we study integrability aspects of the current algebra representation and the factorized quantum nonlinear Schrödinger type dynamical systems, initiated before by G. Goldin with collaborators, in suitably renormalized Fock type Hilbert spaces. There is developed the current algebra representation scheme of reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space. There is presented its application to constructing quantum factorized Hamiltonian systems and their 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 one-dimensional models as the Calogero–Moser–Sutherland and Nonlinear Schrödinger dynamical systems of spin-less Bose-particles.
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ACKNOWLEDGMENTS
Authors would like to convey their warm thanks to Profs. Gerald Goldin, Joel Lebowitz, Denis Blackmore, Maciej Błaszak and Anatol Odziewicz for instructive discussions, useful comments and remarks. Special authors appreciations belongs to Prof. Joel Lebowitz for invitations to take part in the 121st Statistical Mechanics Conference held on May 12–14, 2019 in the Rutgers University, New Brunswick, NJ, USA. The authors’ acknowledgements belong to the Department of Physics, Mathematics and Computer Science of the Cracov University of Technology for a local research grant F-2/370/2018/DS.
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On memory of N.N. Bogolubov, a mathematical physics giant of the XXth century—on his 110th Birthday Jubilee
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Bogolubov, N.N., Prorok, D. & Prykarpatski, A.K. Integrability Aspects of the Current Algebra Representation and the Factorized Quantum Nonlinear Schrödinger Type Dynamical Systems. Phys. Part. Nuclei 51, 434–442 (2020). https://doi.org/10.1134/S1063779620040152
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DOI: https://doi.org/10.1134/S1063779620040152