Integrable Quantum Mappings

Details Integrable Quantum Mappings Integrable Quantum Mappings

1994-09-02

arxiv.org/abs/solv-int/9409001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, to appear in Proceedings of the Intl. Workshop on Symmetries and Integrability of Difference Equations, eds. D. Levi

Scientific paper

We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples we consider quantum mappings associated with the lattice analogues of the KdV and MKdV equations. These mappings possess a non-ultralocal quantum Yang-Baxter structure leading to the existence of commuting families of exact quantum invariants. We derive the associated quantum Miura transformations between these mappings and the corresponding quantum bi-Hamiltonian structure.

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