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Quantum mechanics andp-adic numbers

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Abstract

We study the possibility of representing the proposition lattice associated with a quantum system by a linear vector space with coefficients from ap-adic field. We find inconsistencies if the lattice is assumed, as usual, to be irreducible, complete, orthocomplemented, atomic, and weakly modular.

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References

  1. E. C. G. Stueckelberg et al.,Helv. Phys. Acta 33, 727 (1960);34, 621, 675 (1961);35, 673 (1962). D. Finkelstein, J. M. Jauch, and D. Speiser,J. Math. Phys. 3, 207 (1962);4, 136, 788 (1963).

    Google Scholar 

  2. J. M. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, Mass., 1968); V. S. Varadarajan,Geometry of Quantum Theory (D. Van Nostrand, Princeton, N.J., 1968).

    Google Scholar 

  3. G. Bachman,An Introduction to p-adic Numbers and Valuation Theory (Academic Press, New York, 1964).

    Google Scholar 

  4. O. T. O'Meara,Introduction to Quadratic Forms (Springer-Verlag, Berlin, 1963).

    Google Scholar 

  5. G. Cassinelli, Thesis, University of Genoa.

  6. N. Jacobson,Lectures in Abstract Algebra (D. Van Nostrand, Princeton, N.J., 1951), Vol. I.

    Google Scholar 

  7. J. P. Eckmann and P. C. Zabey,Helv. Phys. Acta 42, 420 (1969).

    Google Scholar 

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Authors and Affiliations

  1. Istituto di Scienze Fisiche dell'Università di Genova, Italy

    E. G. Beltrametti & G. Cassinelli

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Italy

    E. G. Beltrametti & G. Cassinelli

Authors
  1. E. G. Beltrametti
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  2. G. Cassinelli
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Beltrametti, E.G., Cassinelli, G. Quantum mechanics andp-adic numbers. Found Phys 2, 1–7 (1972). https://doi.org/10.1007/BF00708614

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  • DOI: https://doi.org/10.1007/BF00708614

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