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Geometrization of quantum mechanics

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Abstract

We show that various descriptions of quantum mechanics can be represented in geometric terms. In particular, starting with the space of observables and using the momentum map associated with the unitary group, we give a unified geometric description of the different pictures of quantum mechanics. This construction is an alternative to the usual GNS construction for pure states.

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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad de Zaragoza, 50009, Zaragoza, Spain

    J. F. Cariñena

  2. Instituto de Biocomputación y Física de los Sistemas complejos, Universidad de Zaragoza, 50009, Zaragoza, Spain

    J. Clemente-Gallardo

  3. Dipartimento di Scienze Fisiche, Università Federico II di Napoli, INFN, Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Via Cintia, 80126, Napoli, Italy

    G. Marmo

Authors
  1. J. F. Cariñena
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  2. J. Clemente-Gallardo
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  3. G. Marmo
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 20–31, July, 2007.

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Cariñena, J.F., Clemente-Gallardo, J. & Marmo, G. Geometrization of quantum mechanics. Theor Math Phys 152, 894–903 (2007). https://doi.org/10.1007/s11232-007-0075-3

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