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Fuzzy topology and geometric quantum formalism

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Abstract

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of geometric quantum formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty σ x . It’s shown that m evolution with minimal number of additional assumptions obeys to schroedinger and dirac formalisms in norelativistic and relativistic cases correspondingly. It’s argued that particle’s interactions on such fuzzy manifold should be gauge invariant.

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References

  1. A. Connes, Noncommutative Geometry (Academic Press, N.Y., 1994).

    MATH  Google Scholar 

  2. A. P. Balachandran, S. Kurkcuoglu, and S. Vaidia, Lectures on Fuzzy and Fuzzy SUSY Physics (World Scientific, Singapoure, 2007).

    Book  MATH  Google Scholar 

  3. J. Madore, “Fuzzy sphere,” Class. Quant. Gravity 9, 69–83 (1992).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. C. Zeeman, “Topology of brain and visual perception,” in Topology of 3-Manifolds (Prentice-Hall, New Jersey, 1961), pp. 240–248.

    Google Scholar 

  5. C. T. Dodson, “Tangent structures for hazy space,” J. London Math. Soc. 2, 465–474 (1975).

    Article  MathSciNet  Google Scholar 

  6. S. Mayburov, “Fuzzy geometry of phase space and quantization of massive fields,” J. Phys., Ser. A 41, 164071–164080 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Mayburov, “Fuzzy space-time geometry and particle’s dynamics,” Int. J. Theor. Phys. 49, 3192–3198 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  8. L. D. Landau and E. M. Lifshitz, Mechanics of Continuous Media (Pergamon Press, Oxford, N.Y., 1976).

    Google Scholar 

  9. V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1971).

    Google Scholar 

  10. T. Jordan, “Assumptions that imply quantum mechanics is linearm,” Phys. Rev., Ser. A 73, 022101 (2006).

    Article  ADS  Google Scholar 

  11. J. M. Jauch, “Foundations of Quantum Mechanics (Addison-Wesly, Reading, 1968).

    MATH  Google Scholar 

  12. D. I. Blokhintsev, Space-Time in the Microworld (Springer, Berlin, 1973).

    Book  Google Scholar 

  13. T. Cheng and L. Li, Gauge Theory of Elementary Particles (Claredon, Oxford, 1984).

    Google Scholar 

Download references

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Authors and Affiliations

  1. Lebedev Inst. of Physics, Leninsky Prospect 53, Moscow, RU-117924, Russia

    S. N. Mayburov

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  1. S. N. Mayburov
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Correspondence to S. N. Mayburov.

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Mayburov, S.N. Fuzzy topology and geometric quantum formalism. Phys. Part. Nuclei Lett. 11, 1023–1027 (2014). https://doi.org/10.1134/S1547477114070322

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