A1 Refereed original research article in a scientific journal
A THEOREM OF SOLER, THE THEORY OF SYMMETRY AND QUANTUM MECHANICS
Authors: Cassinelli G, Lahti P
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
Publication year: 2012
Journal: International Journal of Geometric Methods in Modern Physics
Journal name in source: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Journal acronym: INT J GEOM METHODS M
Article number: ARTN 1260005
Number in series: 2
Volume: 9
Issue: 2
Number of pages: 7
ISSN: 0219-8878
DOI: https://doi.org/10.1142/S0219887812600055
Abstract
A classical problem in axiomatic quantum mechanics is deducing a Hilbert space realization for a quantum logic that admits a vector space coordinatization of the Piron-McLaren type. Our aim is to show how a theorem of M. Soler [Characterization of Hilbert spaces by orthomodular spaces, Comm. Algebra 23 (1995) 219-243.] can be used to get a (partial) solution of this problem. We first derive a generalization of the Wigner theorem on symmetry transformations that holds already in the Piron-McLaren frame. Then we investigate which conditions on the quantum logic allow the use of Soler's theorem in order to obtain a Hilbert space solution for the coordinatization problem.
A classical problem in axiomatic quantum mechanics is deducing a Hilbert space realization for a quantum logic that admits a vector space coordinatization of the Piron-McLaren type. Our aim is to show how a theorem of M. Soler [Characterization of Hilbert spaces by orthomodular spaces, Comm. Algebra 23 (1995) 219-243.] can be used to get a (partial) solution of this problem. We first derive a generalization of the Wigner theorem on symmetry transformations that holds already in the Piron-McLaren frame. Then we investigate which conditions on the quantum logic allow the use of Soler's theorem in order to obtain a Hilbert space solution for the coordinatization problem.
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