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Many-Particle Schrödinger Type Finitely Factorized Quantum Hamiltonian Systems and Their Integrability

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Geometric Methods in Physics XXXVIII

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We develop G. A. Goldin and D. H. Sharp’s quantum current algebra approach to many-particle Hamiltonian operators. We demonstrate its deep relationship to the Hamiltonian operators’ factorized structure. We investigate this for completely integrable spinless systems, showing the connection with the classical Bethe ansatz ground state representation. The quantum Hamilton operators are considered for integrable delta-potential and oscillatory Caloger-Moser-Sutherland models.

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Acknowledgements

Authors would like to thank Prof. Gerald Goldin for valuable discussions of this work during the XXXVIII International Workshop on “Geometry in Physics”. They also are cordially appreciative of Profs. Joel Lebowitz, Denis Blackmore and Nikolai N. Bogolubov (Jr.) for instructive discussions, useful comments and remarks on the work. A special author’s appreciation belongs to Prof. Joel Lebowitz for the invitation to take part in the 121-st Statistical Mechanics Conference at the Rutgers University, New Brunswick, NJ, USA. Personal A.P.’s acknowledgments belong to the Department of Physics, Mathematics and Computer Science of the Cracow University of Technology for a local research grant F-2/370/2018/DS.

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Authors and Affiliations

  1. Department of Physics and Computer Science, AGH University of Science at Technology, Kraków, Poland

    Dominik Prorok

  2. The Institute of Mathematics, Department of Physics, Mathematics and Computer Science, The Cracow University of Technology, Kraków, Poland

    Anatolij Prykarpatski

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  1. Dominik Prorok
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Correspondence to Anatolij Prykarpatski .

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  1. Departamento de Física, CINVESTAV, Ciudad de México, Mexico

    Piotr Kielanowski

  2. Institute of Mathematics, University of Białystok, Białystok, Poland

    Anatol Odzijewicz

  3. Department of Mathematics and Statistics, Boston University, Boston, MA, USA

    Emma Previato

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Prorok, D., Prykarpatski, A. (2020). Many-Particle Schrödinger Type Finitely Factorized Quantum Hamiltonian Systems and Their Integrability. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXVIII. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-53305-2_16

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