A THEOREM OF SOLER, THE THEORY OF SYMMETRY AND QUANTUM MECHANICS



: Cassinelli G, Lahti P

Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

: 2012

: International Journal of Geometric Methods in Modern Physics

: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

: INT J GEOM METHODS M

: ARTN 1260005

: 2

: 9

: 2

: 7

: 0219-8878

DOI: https://doi.org/10.1142/S0219887812600055


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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