Quantum and Classical Integrable Systems

Details Quantum and Classical Integrable Systems Quantum and Classical Integrable Systems

1997-03-12

arxiv.org/abs/q-alg/9703023v1

Mathematics

Quantum Algebra

59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter School on Nonlinear Systems, Pondicherry, January 1996

Scientific paper

10.1007/BFb0113700

The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the universal enveloping algebra of an affine Lie algebra, or its q-deformation.) A similar relation also holds in the classical case. We discuss different guises of this very important relation and its implication for the description of the spectrum and the eigenfunctions of the quantum system. Parallels between the classical and the quantum cases are thoroughly discussed.

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