Integrable Quantum Mappings
solv-int
2008-02-03 v1 Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.solv-int/9409001,
title = {Integrable Quantum Mappings},
author = {H. W. Capel and F. W. Nijhoff},
journal= {arXiv preprint arXiv:solv-int/9409001},
year = {2008}
}
Comments
13 pages, to appear in Proceedings of the Intl. Workshop on Symmetries and Integrability of Difference Equations, eds. D. Levi, L. Vinet and P. Winternitz