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Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices

2. Completely Integrable Systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 925)

Abstract

We consider quantum Hamiltonian systems of lattice type which are associated with classical finite dimensional Lie algebras (like MH(2), SO(3) etc.), and possess complete integrability properties. These Hamiltonian systems are written in canonical Heisenberg pn, qn variables. They have factorized S-matrices and are generalizations of the quantum Toda lattice Hamiltonian as well as XYZ-models of statistical mechanics.

Keywords

  • Commutation Relation
  • Poisson Bracket
  • Symplectic Manifold
  • Formal Power Series
  • Casimir Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1982 Springer-Verlag

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Chudnovsky, D., Chudnovsky, G. (1982). Quantum Hamiltonians associated with finite-dimensional Lie algebras and factorized s-matrices. In: Chudnovsky, D.V., Chudnovsky, G.V. (eds) The Riemann Problem, Complete Integrability and Arithmetic Applications. Lecture Notes in Mathematics, vol 925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093506

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  • DOI: https://doi.org/10.1007/BFb0093506

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11483-3

  • Online ISBN: 978-3-540-39152-4

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