Remarks on the GNS Representation and the Geometry of Quantum States-Reference-Cited by-同舟云学术

Remarks on the GNS Representation and the Geometry of Quantum States

Published:2009-09 Issue:02n03 Volume:16 Page:157-177
ISSN:1230-1612
Container-title:Open Systems & Information Dynamics
language:en
Short-container-title:Open Syst. Inf. Dyn.

Author:

Chruściński Dariusz¹,Marmo Giuseppe²³

Affiliation:

1. Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87–100 Toruń, Poland

2. Dipartamento di Scienze Fisiche, Universitá "Federico II" di Napoli, Complesso Universitario di Monte Sant Angelo, Via Cintia, I-80126 Napoli, Italy

3. Instituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte Sant Angelo, Via Cintia, I-80126 Napoli, Italy

Abstract

It is shown how to introduce a geometric formulation of the algebraic approach to the standard non-relativistic quantum mechanics. It turns out that the GNS representation provides not only symplectic but even 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1230161209000128

Reference35 articles.

1. Postulates for General Quantum Mechanics

2. Complex Coordinates and Quantum Mechanics

3. Geometrization of quantum mechanics

4. Aspetti geometrici dei sistemi di tipo quantistico

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