Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Singularities in the classical theory of topological transitions

Abstract

Within the framework of classical (nonquantum) theory of topological transitions, the problem of singularities is discussed; this is one of the basic obstacles to transition to a quantum description. The features of the solution of this problem for a gravitational field and the fields of the sources are considered. In the first case, the singularity problem may be solved by constructing a Lagrangian that is regular in the vicinity of the topological transition. For gravitational-field sources this method is inapplicable, and therefore it is necessary either to use a mechanism analogous to the mechanism of spontaneous symmetry violation or to introduce additional boundary conditions which ensure regularity of the Lagrangian and the field equations.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    J. Wheeler, Einstein's Forecasts [Russian translation], Mir, Moscow (1970).

  2. 2.

    D. Brill and R. Goudi, in: Quantum Gravitation and Topology [Russian translation], Mir, Moscow (1973), p. 66–179.

  3. 3.

    B. S. De Witt, in: General Relativity and Gravitation. Invited Papers and Discussion Reports of 10th International Conference, B. Bertotti (ed.,), Padua, July 3–8, 1983, Padua (1984), pp. 439–451; Proceedings of Third Seminar on Quantum Gravity, M. A. Markov et al. (eds.), Moscow, October 23–25, 1984, World Sei., Singapore (1985), pp. 103–122.

  4. 4.

    T. Banks, Nucl. Phys.,B249, No. 2, 332–360 (1985).

  5. 5.

    R. D. Sorkin, Phys. Rev. D,D33, No. 4, 978–982 (1986).

  6. 6.

    M. Yu. Konstantinov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12, 42–46 (1983).

  7. 7.

    M. Yu. Konstantinov and V. N., Mel'nikov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 8, 32–36 (1984); Problems of Gravitation and Elementary-Particle Theory [in Russian], Énergoatomizdat, Moscow (1985), No. 15, pp. 45–51.

  8. 8.

    M. Yu. Konstantinov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 1, 96–100 (1985).

  9. 9.

    M. Yu. Konstantinov, in: Problems of Gravitation and Elementary-Particle Theory [in Russian], Énergoatomizdat, Moscow (1985), No. 16, pp. 148–157.

  10. 10.

    M. Yu. Konstantinov and V. N. Melnikov, Class. Quant. Gravity,3, No. 3, 401–416 (1986).

  11. 11.

    A. T. Fomenko, Differential Geometry and Topology. Additional Chapters [in Russian], Moscow State Univ., Moscow (1983).

  12. 12.

    K. P. Stanyukovich and V. N. Mel'nikov, Hydrodynamics, Fields, and Constants in the Theory of Gravitation [in Russian], Énergoatomizdat, Moscow (1983).

  13. 13.

    K. P. Stanyukovich, Gravitational Field and Elementary Particles [in Russian], Nauka, Moscow (1965).

  14. 14.

    A. Vilenkin, Phys. Rev. D,D27, 2848 (1983).

  15. 15.

    C. M. Will, Theory and Experiment in Gravitational Physics, Cambridge Univ. Press (1981).

Download references

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 35–40, December, 1988.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Konstantinov, M.Y. Singularities in the classical theory of topological transitions. Soviet Physics Journal 31, 982–985 (1988). https://doi.org/10.1007/BF01101166

Download citation

Keywords

  • Boundary Condition
  • Field Equation
  • Classical Theory
  • Gravitational Field
  • Singularity Problem