Remarks on the GNS Representation and the Geometry of Quantum States

Details Remarks on the GNS Representation and the Geometry of Quantum States Remarks on the GNS Representation and the Geometry of Quantum States

2008-10-09

arxiv.org/abs/0810.1660v1

Open Syst.Info.Dyn.16:157-177,2009

Physics

Mathematical Physics

20 pages

Scientific paper

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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