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On physics at the Planck scale: Space as a network

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Abstract

It is shown that the one-dimensional quantum field theory can be modeled as a chain of classical oscillators in a thermal bath provided that the Gibbs measure is identified with the phase-space volume measure, the chain being in a nonequilibrium state. Quantized strings and p-branes are also modeled by ordered systems of oscillators. The model of a one-dimensional superspace is constructed. It is shown that the Ramond-Neveu-Schwarz superstring is modeled by a helix formed of a bosonic-string in a multidimensional space. The physical 3D space is represented by a superstring structure (3D “network”), which is described by some Lagrangian. Thus, the unified description of all interactions including gravity is achieved because the superstring excitations involve all fields. In view of the discrete character of the initial structure, the theory is free of ultraviolet divergences. The essential element of the model is the occurrence of the cosmological constant in the gravity equations. A black hole model giving reasonable values for its temperature and entropy is proposed.

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References

  1. M. B. Green, J H. Schwarz, and E. Witten, Superstring Theory (Cambridge Univ. Press, Cambridge, 1987; Mir, Moscow, 1990).

    MATH  Google Scholar 

  2. A. Strominger and C. Vafa, Phys. Lett. B 379, 99 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  3. S. W. Hawking, Phys. Rev. D 14, 2460 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  4. G. ’t Hooft, Class. Quant. Grav. 16, 3263 (1999).

    Article  MATH  ADS  Google Scholar 

  5. L. V. Prokhorov, Yad. Fiz. 67, 1322 (2004) [Phys. At. Nucl. 67, 1299 (2004)].

    Google Scholar 

  6. L. V. Prokhorov, “Quantum Mechanics As Kinetics,” quant-ph/0406079.

  7. P. A. M. Dirac, Lectures on Quantum Field Theory (Mir, Moscow, 1971) [in Russian].

    Google Scholar 

  8. F. Strocchi, Rev. Mod. Phys. 38, 36 (1966).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. Ya. G. Sinai, Introduction into Ergodic Theory (FAZIS, Moscow, 1996) [in Russian].

    Google Scholar 

  10. L. V. Prokhorov, Vestn. SPbGU, Ser. 4. 4, 3 (2005).

    Google Scholar 

  11. A. M. Perelomov, Generalized Coherent States and Their Applications (Nauka, Moscow, 1987; Springer-Verlag, New York, 1986).

    Google Scholar 

  12. V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961).

    Article  MATH  MathSciNet  Google Scholar 

  13. N. Hurt, Geometric Quantization in Action (Reidel, Dordrecht, 1983; Mir, Moscow, 1985).

    MATH  Google Scholar 

  14. B. A. Koopman, Proc. Nat. Acad. Sci. U.S.A. 17, 315 (1931).

    Article  MATH  ADS  Google Scholar 

  15. J. Neumann, Ann. Math 33, 587 (1932).

    Article  Google Scholar 

  16. M. Loeve, Probability Theory (D. van Nostrand, Princeton, 1960).

    MATH  Google Scholar 

  17. L. V. Prokhorov, Usp. Fiz. Nauk 154, 299 (1988) [Phys. Usp. 31, 151 (1988)].

    MathSciNet  Google Scholar 

  18. L. V. Prokhorov, Fiz. Elem. Chastits At. Yadra 31, 47 (2000) [Phys. Part. Nucl. 31, 22 (2000)].

    Google Scholar 

  19. B. M. Barbashov and V. V. Nesterenko, The Relativistic String Model and Hadron Physics (Energoatomizdat, Moscow, 1987; World Scientific, Singapore, 1989).

    Google Scholar 

  20. A. V. Golovnev and L. V. Prokhorov, Int. J. Theor. Phys. 45, 942 (2006).

    Article  MathSciNet  Google Scholar 

  21. Yu. A. Golfand and E. P. Likhtman, Pisma Zh. Eksp. Teor. Fiz. 13, 452 (1971) [JETP Lett. 13, 323 (1971)].

    Google Scholar 

  22. J.-L. Gervais and B. Sakita, Nucl. Phys. B 34, 632 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  23. D. V. Volkov and V. P. Akulov, Pisma Zh. Eksp. Teor. Fiz. 16, 621 (1972) [JETP Lett. 16, 438 (1972)].

    Google Scholar 

  24. J. Wess and B. Zumino, Nucl. Phys. 70, 39 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  25. R. C. T. da Costa, Phys. Rev. A 23, 1982 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  26. L. V. Prokhorov, in Proc. of VI Int. Conf. on Path Integrals, Florence, 1998 (World Scientific, London, 1999), p. 249.

    Google Scholar 

  27. N. H. Fletcher, Am. J. Phys 72, 701 (2004).

    Article  ADS  Google Scholar 

  28. P. Ramond, Phys. Rev. D 3, 2415 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  29. A. Neveu and J. H. Schwarz, Nucl. Phys. B 31, 86 (1971).

    Article  ADS  Google Scholar 

  30. M. Green and J. H. Schwarz, Nucl. Phys. B 198, 252 (1982).

    Article  ADS  Google Scholar 

  31. M. Green and J. H. Schwarz, Phys. Lett. B 136, 367 (1984).

    Article  ADS  Google Scholar 

  32. Th. Kaluza, Sitzungsber. Preuss. Akad. Wiss. Math. Phys. Kl. (1921), p. 966.

  33. O. Klein, Zs. f. Phys. 37, 895 (1926).

    Article  Google Scholar 

  34. H. Mandel, Zs. f. Phys. 39, 136 (1926).

    Article  Google Scholar 

  35. V. Fock, Zs. f. Phys. 39, 226 (1926).

    Article  Google Scholar 

  36. V. F. Mukhanov, Pisma Zh. Eksp. Teor. Fiz. 44, 50 (1986) [JETP Lett. 44, 63 (1986)].

    MathSciNet  Google Scholar 

  37. Ya. I. Kogan, Pisma Zh. Eksp. Teor. Fiz. 44, 209 (1986) [JETP Lett. 44, 267 (1986)].

    Google Scholar 

  38. N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Today 2, 35 (2002).

    Article  Google Scholar 

  39. L. V. Prokhorov, “Quantum Mechanics and the Cosmological Constant,” gr-qc/0602023.

  40. A. G. Riess et al., Astron. J. 116, 1009 (1998); S. Perlmutter, et al., Astrophys. J. 517, 565 (1999).

    Article  ADS  Google Scholar 

  41. B. M. Barbashov, V. N. Pervushin, and D. V. Proskurin, Fiz. Elem. Chastits At. Yadra 34, 138 (2003) [Phys. Part. Nucl. 34, S68 (2003)].

    Google Scholar 

  42. D. C. Tsui, H. L. Störmer, A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).

    Article  ADS  Google Scholar 

  43. R. de-Picciotto et al., Nature 389, 162 (1997); M. Reznikov et al., Nature 399, 238 (1999).

    Article  ADS  Google Scholar 

  44. J. R. Klauder and S. V. Shabanov, Nucl. Phys. B 511, 713 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  45. P. A. M. Dirac, Lectures on Quantum Mechanics (New York, 1964; Mir, Moscow, 1968).

  46. L. D. Faddeev and S. L. Shatashvili, Phys. Lett. B 167, 225 (1986).

    Article  ADS  Google Scholar 

  47. A. G. Nuramatov and L. V. Prokhorov, Int. J. Geom. Meth. Mod. Phys. 3, 1459 (2006); quant-ph/0507038.

    Article  MATH  MathSciNet  Google Scholar 

  48. A. V. Golovnev, “Thin Layer Quantization in Higher Dimensions,” quant-ph/0508111.

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Authors and Affiliations

  1. Fock Institute of Physics, St. Petersburg State University, ul. Ul’yanovskaya 1, Petrodvorets, 198504, Russia

    L. V. Prokhorov

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  1. L. V. Prokhorov
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Original Russian Text © L.V. Prokhorov, 2007, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2007, Vol. 38, No. 3.

Extended version of lectures read at the Fock International School of Physics, St. Petersburg, 2004.

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Prokhorov, L.V. On physics at the Planck scale: Space as a network. Phys. Part. Nuclei 38, 364–383 (2007). https://doi.org/10.1134/S1063779607030045

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