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arXiv · 0810.1660

Remarks on the GNS Representation and the Geometry of Quantum States

Dariusz Chruscinski·Giuseppe Marmo
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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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Dariusz Chruscinski, Giuseppe Marmo. 2008-10-09. Remarks on the GNS Representation and the Geometry of Quantum States. https://arxiv.org/abs/0810.1660

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