Towards a definition of quantum integrability

Details Towards a definition of quantum integrability Towards a definition of quantum integrability

2008-08-28

arxiv.org/abs/0808.3819v1

Int.J.Geom.Meth.Mod.Phys.6:129-172,2009

Physics

Mathematical Physics

37 pages, AmsLatex, 1 figure

Scientific paper

10.1142/S0219887809003448

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.

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