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Classical and Quantum Nonultralocal Systems on the Lattice

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Algebraic Aspects of Integrable Systems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 26))

Abstract

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.

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Author information

Authors and Affiliations

  1. Université de Bourgogne Physique Mathématique, B.P. 138, 21004, Dijon CEDEX, France

    Michael Semenov-Tian-Shansky

  2. Steklov Mathematical Institute, St. Petersburg, Russia

    Michael Semenov-Tian-Shansky & Alexey Sevostyanov

Authors
  1. Michael Semenov-Tian-Shansky
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  2. Alexey Sevostyanov
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College, SW7 2BZ, London, UK

    A. S. Fokas

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    I. M. Gelfand

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© 1997 Birkhäuser Boston

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Semenov-Tian-Shansky, M., Sevostyanov, A. (1997). Classical and Quantum Nonultralocal Systems on the Lattice. In: Fokas, A.S., Gelfand, I.M. (eds) Algebraic Aspects of Integrable Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 26. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2434-1_17

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  • DOI: https://doi.org/10.1007/978-1-4612-2434-1_17

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7535-0

  • Online ISBN: 978-1-4612-2434-1

  • eBook Packages: Springer Book Archive

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