International Journal of Theoretical Physics

, Volume 35, Issue 3, pp 593–604 | Cite as

Topologimeter and the problem of physical interpretation of topology lattice

  • A. A. Grib
  • R. R. Zapatrin


The collection of all topologies on the set of three points is studied, treating the topology as a quantum-like observable. This turns out to be possible under the assumption of the asymmetry between the spaces of bra and ket vectors. Analogies between the introduced topologimeter and Stem-Gerlach experiments are outlined.


Field Theory Elementary Particle Quantum Field Theory Physical Interpretation Topology Lattice 
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  1. Birkhoff, G., and von Neumann, J. (1936). The logic of quantum mechanics,Annals of Mathematics,37, 923.Google Scholar
  2. D'Espagnat, B. (1976).Conceptual Foundations of Quantum Mechanics, Benjamin, New York.Google Scholar
  3. Grib, A. A., and Zapatrin, R. R. (1992). Topology lattice as quantum logic,International Journal of Theoretical Physics,31, 1093.Google Scholar
  4. Larson, R. F., and Andima, S. (1975). The lattice of topologies: A survey.Rocky Mountain Journal of Mathematics,5, 177.Google Scholar
  5. Leinaas, J., and Myrheim, R. (1991). Quantum theories for identical particles.International Journal of Modern Physics B. 5, 2573.Google Scholar
  6. Sorkin, R. (1991). Finitary substitutes for continuous topology,International Journal of Theoretical Physics,30, 930.Google Scholar
  7. Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.Google Scholar
  8. Zapatrin, R. R. (1993). Pre-Regge calculus: Topology via logic,International Journal of Theoretical Physics,32, 779.Google Scholar
  9. Zapatrin, R. R. (1994). Quantum logic without negation,Helvetica Physica Acta,67, 188.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • A. A. Grib
    • 1
  • R. R. Zapatrin
    • 2
  1. 1.A. A. Friedmann Laboratory for Theoretical PhysicsSt-PetersburgRussia
  2. 2.Department of MathematicsSt. Petersburg University of Economics and FinanceSt. PetersburgRussia

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