Foundations of Physics Letters

, Volume 9, Issue 3, pp 295–300 | Cite as

Non-standard aspects of Minkowski causal logic

  • Antonio Zecca


The Minkowski causal logic, which is already known to be a complete orthomodular lattice, is found to be also an atomistic and irreducible logic, but to have no other essential properties to be represented in terms of all the subspace of some Hilbert space. Alternative representation of the logic in terms of subspaces of a real vector space or of the states in terms of probability measures are suggested.

Key words

Minkowski causal logic 


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  1. 1.
    E. C. Zeeman,J. Math. Phys. 5, 4901 (1964).Google Scholar
  2. 2.
    G. Barucchi and G. Teppati,Nuovo Cimento 52A, 50 (1967).Google Scholar
  3. 3.
    G. Teppati,Nuovo Cimento 54A, 800 (1968).Google Scholar
  4. 4.
    J. L. Alonso and F. Y. Indurain,Comm. Math. Phys. 4, 349 (1967).Google Scholar
  5. 5.
    A. D. Alexandrov,Can. J. Math. 19, 1119 (1967).Google Scholar
  6. 6.
    C. Gheorghe and E. Mihul,Comm. Math. Phys. 14, 165 (1969).Google Scholar
  7. 7.
    H. J. Borchers and G. C. Hegerfeldt,Comm. Math. Phys. 28, 259 (1972).Google Scholar
  8. 8.
    A. A. Blasi, F. Gallone, V. Gorini, and A. Zecca,Nuovo Cimento 10A, 19 (1972).Google Scholar
  9. 9.
    W. Cegla and A. Z. Jadczyk,Rep. Math. Phys. 9, 377 (1976).Google Scholar
  10. 10.
    W. Cegla and A. Z. Jadczyk,Comm. Math. Phys. 57, 213 (1977).Google Scholar
  11. 11.
    D. J. Foulis and C. H. Randall,Combinatorial Theory 11, 157 (1971).Google Scholar
  12. 12.
    D. J. Foulis and C. H. Randall, “The empirical logic approach to the physical sciences,” inFoundations of Quantum Mechanics and Ordered Linear Spaces A. Hartkämper and H. Neumann, eds. (Springer, Berlin, 1972).Google Scholar
  13. 13.
    D. J. Foulis, and C. H. Randall,J. Math. Phys. 13, 1667 (1972).Google Scholar
  14. 14.
    J. M. Jauch,Foundations of Quantum Mechanics (Addison Westley, Reading, Massachusetts, 1968).Google Scholar
  15. 15.
    W. Cegla and A. Z. Jadczyk,Lett. Math. Phys. 3, 109 (1979).Google Scholar
  16. 16.
    A. Borowiec and A. Z. Jadczyk,Lett. Math. Phys. 3, 255 (1979).Google Scholar
  17. 17.
    P. C. Deliyannis,J. Math. Phys. 14, 249 (1973).Google Scholar
  18. 18.
    V. S. Varadarajan,Geometry of Quantum Theory, Vol. I (Van Nostrand, Toronto, 1968).Google Scholar
  19. 19.
    W. Cegla, inCurrent Issues in Quantum Logic, E. Beltrametti and B. C. Van Fraassen, eds. (Plenum, New York, 1981).Google Scholar
  20. 20.
    F. Maeda and S. Maeda,Theory of Symmetric Lattices (Springer, Berlin, 1970).Google Scholar
  21. 21.
    E. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1981).Google Scholar
  22. 22.
    A. Zecca,Int. J. Theor. Phys. 20, 191 (1981).Google Scholar
  23. 23.
    C. Piron,Helv. Phys. Acta 37, 439 (1964).Google Scholar
  24. 24.
    I. Amemiya and H. Araki,Publications of the Research Institute for Mathematical Sciences (Kyoto University) A2, 423 (1967).Google Scholar
  25. 25.
    C. Piron,Foundations of Quantum Physics (Benjamin, Reading, Massachusetts, 1976).Google Scholar
  26. 26.
    J. Dixmier,Les Algebres d' Operateurs dans l' espace Hilbertienne (Gauthier-Villars, Paris, 1969).Google Scholar
  27. 27.
    S. Sakai,C*-Algebras and W*-Algebras (Springer, Berlin, 1970).Google Scholar
  28. 28.
    P. C. Deliyannis,J. Math. Phys. 17, 248 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Antonio Zecca
    • 1
  1. 1.Dipartimento di Fisica dell' Universitá di Milano and INFNSezione di MilanoMilanoItaly

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