A topological interpretation of quantum theory and elementary particle structure

V.M. Zhuravlev1

Abstract

We present a new concept of topological and geometric interpretation of quantum mechanics. A special choice of geometric markers makes it possible to connect quantum mechanics with a topological interpretation of the electric charge and to build an electrodynamics with integer-valued point charges. The electric charge gains the status of a topological charge in the form of a geometrically distinguished region of the physical space with nonzero curvature. We introduce a topological interpretation of particles and compare it with elementary particle properties. A topological interpretation of the baryonic charge is suggested.

References

  1. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Methods of Homology Theory (Nauka, Moscow, 1984, in Russian).
  2. J. Kokkedee, Theory of the Quark Model (W. A. Benjamin, New York - Amsterdam, 1969).
  3. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Methods and Applications (Nauka, Moscow, 1979, in Russian).
  4. M. W. Hirsh, Differential Topology (Springer-Verlag, New York - Heidelberg - Berlin, 1976).
  5. A. Ya. Burinskii, Phys. Rev. D 67, 124024 (2003), gr-qc/0212048.
  6. V. V. Kassandrov, in: Space-Time Structure: Algebra and Geometry, (Ed. D. G. Pavlov et al. - Lilia Print, Moscow, 2007, p. 422), hep-th/0312278; Physics of Atomic Nuclei 72 (5), 813-827 (2009), arXiv: 0907.5425.
  7. M. M. Postnikov, Introduction to the Morse Theory, (Nauka, Moscow, 1971, in Russian).
  8. Yu. P. Rybakov and V. i. Sanyuk, Multidimensional Solitons (RUDN Press, 2001, in Russian).
  9. A. Sadbury, Quantum Mechanics and the Particles of Nature (Cambrige Univ. Press, Cambridge, 1986),
  10. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, 1955).
  11. I. S. Shapiro and M. A. Olshanetsky, in: Elementary Particles (Sixth ITEF School, 1979, 4th issue, p. 5) (in Russian).
  12. A. H. Wallace, Differential Topology. First Steps (Univ. of Pennsylvania, W. A. Benjamin, New York - Amsterdam, 1968).
  13. J. W. Milnor, Topology from the Differentiable Viewpoint (Princeton Univ., based on notes by David W. Weaver, Univ. of Virginia, Charlottesville. 1965).
  14. V. M. Zhuravlev, Electrodynamics with integer-valued charges and topology. Izv. Vuzov, Fiz., No. 2 (2000).
  15. V. M. Zhuravlev, Electrodynamics with integer-valued charges, topology, and elementary particle structure. In: Critical Technologies and Basic Problems of Condensed Matter Physics (Ulyanovsk, UlGU press, 2001, pp. 42-72). (in Russian).
  16. V. M. Zhuravlev, Electrodynamics with integer-valued charges and topology, Proc. Int. Conf. "Gravitation and Electromagnetism" (Minsk, BGU press, 1998, pp. 42-50).
  17. A. S. Shvarts, Quantum Field Theory and Topology (Nauka, Moscow, 1989) (in Russian).
  18. Yu. S. Vladimirov, A Relational Theory of Space-Time and Interactions. Part 1, 2 (Moscow State University Press, 1998) (in Russian).
  19. R. Sorkin, J. Phys. A 10, 717 (1977).
  20. A. D. Sakharov, in: Problems of Theoretical Physics (Nauka, Moscow, 1972, p. 242) (in Russian).
  21. Ch. Misner and J. Wheeler, Ann. of Phys. 2, 525 (1957)
  22. J. A. Wheeler, Neutrinos, Gravitation and Geometry Rend. Scuola intern. fis. "Enrico Fermi" (Verona, 1959), Corso XI, p. 67-196, ed. N. Zanicholli, (Bologna, 1960).
  23. C. W. Misner and J. A. Wheeler, Ann. Phys. (USA) 2, 527 (1957).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page