This article is cited in 49 papers

Geometrization of quantum mechanics

J. F. Carinena^a, J. Clemente-Gallardo^a, G. Marmo<sup>bc

a</sup> University of Zaragoza
^b Università degli Studi di Napoli Federico II
^c INFN — National Institute of Nuclear Physics, Sezione di Napoli

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.

Keywords: quantum mechanics, Hermitian structure, Jordan algebra, Poisson bracket, Lie–Jordan algebra.

DOI: 10.4213/tmf6067

 English version: Theoretical and Mathematical Physics, 2007, 152:1, 894–903

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