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

作者：Cassinelli Gianni^*; Lahti Pekka

来源：International Journal of Geometric Methods in Modern Physics, 2012, 9(2): 1260005.

DOI：10.1142/S0219887812600055

• Quantum logic
• a theorem of Soler
• symmetry
• a Hilbert space realization

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%26apos;s theorem in order to obtain a Hilbert space solution for the coordinatization problem.

• 出版日期2012-3