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