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Remarks on the GNS Representation and the Geometry of Quantum States

Mathematical Physics 2009-11-02 v1 math.MP Quantum Physics

Abstract

It is shown how to introduce a geometric description of the algebraic approach to the non-relativistic quantum mechanics. It turns out that the GNS representation provides not only symplectic but also Hermitian realization of a `quantum Poisson algebra'. We discuss alternative Hamiltonian structures emerging out of different GNS representations which provide a natural setting for quantum bi-Hamiltonian systems.

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Cite

@article{arxiv.0810.1660,
  title  = {Remarks on the GNS Representation and the Geometry of Quantum States},
  author = {Dariusz Chruscinski and Giuseppe Marmo},
  journal= {arXiv preprint arXiv:0810.1660},
  year   = {2009}
}

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20 pages