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Quantum logic axioms and the proposition-state structure

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Abstract

A possible picture of the axiomatic basis of quantum mechanics is drawn and the set of propositions of the quantum logic approach to quantum mechanics is shown to be a complete, orthocomplemented and weakly modular lattice. A condition that the set of propositions be atomic is found, in which the notion of ‘characteristic state” is involved. This scheme is compared with the usual Hilbert one, and in a Hilbert picture in which discrete superselection rules can be present also, the characteristic states are shown to be the pure states.

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Authors and Affiliations

  1. Istituto di Scienze Fisiche dell'Università, 20133, Milano, Italy

    Franco Gallone & Antonio Zecca

Authors
  1. Franco Gallone
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  2. Antonio Zecca
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Additional information

Both authors acknowledge a C.N.R. (Comitato Nazionale per le Scienze Matematiche) scholarship.

Also Scuola di Perfezionamento in Fisica, Università di Milano.

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Gallone, F., Zecca, A. Quantum logic axioms and the proposition-state structure. Int J Theor Phys 8, 51–63 (1973). https://doi.org/10.1007/BF00671579

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  • DOI: https://doi.org/10.1007/BF00671579

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