Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations
Abstract
Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed CalogeroMoser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some elementary linear algebra. The solutions constructed in this way inherit continuous and discrete symmetries from the CM phase space.
 Publication:

arXiv eprints
 Pub Date:
 April 2000
 arXiv:
 arXiv:mathph/0004030
 Bibcode:
 2000math.ph...4030K
 Keywords:

 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Mathematics  Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras
 EPrint:
 to appear in "Regular and Chaotic Dynamics"