Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations

Details Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations

2000-04-24

arxiv.org/abs/math-ph/0004030v1

Physics

Mathematical Physics

to appear in "Regular and Chaotic Dynamics"

Scientific paper

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 Calogero-Moser 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.

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