Skip to main content
SpringerLink
Log in

On Wheeler-De Witt equation in multidimensional cosmology

Об уравнении Вилера- де Витта в многомерной космологии

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The Wheeler-De Witt equation for multidimensional cosmology withn spaces of constant curvature (n>1) is proposed. This equation has a conformally covariant form. Some integrable cases are considered.

Riassunto

Si propone l'equazione di Wheeler-De Witt per la cosmologia multidimensionale conn spazi di curvatura costante (n>1). Questa equazione ha una forma conformemente covariante. Si considerano alcuni casi integrabili.

Резюме

Предлалается уравнение Вилера- де Витта для многомерной космологии сn пространствами постоянной кривизны (n>1). Это уравнение имеет конформно ковариатную форму. Рассматриваются некоторые интегрируемые случаи.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. S. De Witt:Phys. Rev.,160, 1113 (1967).

    Article  ADS  Google Scholar 

  2. V. N. Melnikov andV. A. Reshetov: inProblems of Gravitation and Elementary Particle Theory (VNIIFTRI, Moscow, 1972), p. 117 (in Russian);V. N. Melnikov andM. I. Kalinin in:Abstracts of the III National Gravitational Conference (ErGU, Erevan, 1972), p. 43 (in Russian);K. P. Stanjukovich andV. N. Melnikov:Hydrodynamics, Fields and Constants in the Theory of Gravitation (Energoatomizdat, Moscow, 1983) (in Russian).

    Google Scholar 

  3. J. B. Hartle andS. W. Hawking:Phys. Rev. D,23, 2960 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  4. M. J. Duff, B. F. W. Nilsson andC. N. Pope:Phys. Rep.,130, 1 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  5. J. H. Schwarz:Phys. Rep.,89, 223 (1982);M. B. Green:Surv. High Energy Phys.,3, 127 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  6. J. J. Halliwell:Nucl. Phys. B,266, 228 (1986);286, 729 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  7. R. Laflamme:The Wave Function of a S 1×S2 Universe, D.A.M.T.P. preprint, (Cambridge, (1986)).

  8. J. Louko:Fate of Singularities in Bianchi III Quantum Cosmology. ibid. D.A.M.T.P. preprint, (1987);Semiclassical Path Measure and Factor Ordering in Quantum Cosmology,ibid. D.A.M.T.P. preprint (1988).

  9. S. W. Hawking andD. N. Page:Nucl. Phys. B,264, 185 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  10. T. Christodoulakis andJ. Zanelli:Nuovo Cimento B,93, 1 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  11. T. Christodoulakis andJ. Zanelli:ibid.,,93, 22 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  12. T. Christodoulakis andJ. Zanelli:Class. Quan. Grav.,4, 851 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  13. J. J. Halliwell:Phys. Rev. D,36, 3626 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  14. C. W. Misner: inMagic without Magic: John Archibald Wheeler, editedJ. R. Klauder (Freeman, San Francisco, 1972) p. 441;K. Kuchar, in:Relativity, Astrophysics and Cosmology, edited byW. Israel (D. Reidel, Dordrecht, 1973) p. 237;M. Henneaux, M. Pilati andC. Teitelboim:Phys. Lett. B,110, 123 (1982);T. Christodoulakis andJ. Zanelli:Phys. Rev. D,29, 2738 (1984);Phys. Lett. A,102, 227 (1984).

    Google Scholar 

  15. J. J. Halliwell:Phys. Rev. D,38, 2468 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  16. G. W. Gibbons andS. W. Hawking:Phys. Rev. D,15, 2752 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  17. N. D. Birell andP. C. W. Davies:Quantum Fields in Curved Space (Cambridge University press, Cambridge, Mass., 1982).

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. USSR State Committee for Standards, 9 Leninsky prospect, 117049, Moscow, USSR

    V. D. Ivashchuk & V. N. Melnikov

  2. Department of Physics, University of Odessa, 2 Petra Velikogo, 27000, Odessa, USSR

    A. I. Zhuk

Authors
  1. V. D. Ivashchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Melnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. I. Zhuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Traduzione a cura della Redazione.

Переведено редакцией.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivashchuk, V.D., Melnikov, V.N. & Zhuk, A.I. On Wheeler-De Witt equation in multidimensional cosmology. Nuov Cim B 104, 575–582 (1989). https://doi.org/10.1007/BF02726165

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02726165

Search

Navigation