Special stochastic representation of quantum mechanics and solitons

Authors

  • Yu.P. Rybakov

Keywords:

stochastic representation
solitons
random Hilbert space

Abstract

A special stochastic representation of quantum mechanics is proposed. The basis of this representation is the linear combination of soliton solutions to some nonlinear field equations, the particles being identified with the soliton configurations. The wave function of a particle proves to be a vector in the random Hilbert space. The many-particle wave function is constructed via the many-solitons configurations. It is shown that, in the point-like limit when the proper size of the soliton configuration vanishes, the main principles of quantum mechanics are restored. In particular, the expectation values of physical observables are obtained as the Hermitian forms generated by self-conjugated operators and the spin-statistics correspondence stems from the extended character of particles-solitons.

New computational technologies

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Published

2009-10-26

Issue

Vol. 10 (2009): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biography

Yu.P. Rybakov

Peoples' Friendship University of Russia,
Faculty of Science
• Professor, Head of Department

References

  1. de Broglie L. Les incertitudes d’Heisenberg et l’interpracute etation probabiliste de la macute ecanique ondulatoire. Paris: Gauthier-Villars, 1982.
  2. Einstein A. Collected papers. Moscow: Nauka, 1967.
  3. Snyder H. Quantized space-time // Physical Review. 1947. 71. 38-41.
  4. Yukawa H. On the radius of the elementary particle // Physical Review. 1949. 76. 300-301.
  5. Rybakov Yu.P. On the causal interpretation of quantum mechanics // Found. of Physics. 1974. 4, N 2. 149-161.
  6. Rybakov Yu.P. La thacute eorie statistique des champs et la macute ecanique quantique // Ann. Fond. L. de Broglie. 1977. 2, N 3. 181-203.
  7. Rybakov Yu.P. Self-gravitating solitons and nonlinear-resonance quantization mechanism // Bulletin of Peoples» Friendship University of Russia. Ser. Physics. 1995. 3, N 1. 130-137.
  8. Rybakov Yu.P., Saha B. Soliton model of atom // Found. of Physics. 1995. 25, N 12. 1723-1731.
  9. Rybakov Yu.P., Saha B. Interaction of a charged 3D soliton with a Coulomb center // Physics Letters. Ser. A. 1996. 222, N 1. 5-13.
  10. Rybakov Yu.P., Shachir M. On Fresnel diffraction of solitons in the Synge model // Izvestia VUZov. Ser. Physics. 1982. 25, N 1. 36-38.
  11. Rybakov Yu.P., Terletsky S.A. Dynamics of solitons in external fields and quantum mechanics // Bulletin of Peoples» Friendship University of Russia. Ser. Physics. 2004. 12. 88-112.