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
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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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