Skip to main content
SpringerLink
Log in

Straight-line path approximation for studying Planckian-energy scattering in quantum gravity

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

Summary

A method is proposed for constructing a scattering amplitude in quantum gravity by means of functional integration. The straight-line path approximation is used to calculate the functional integrals required. The closed analytic, relativistically invariant expressions are obtained for the two-particle elastic-scattering amplitudes. In the limit of high energiess→∞ and for given momentum transfers this expression for scattering amplitude takes a Glauber representation with an eikonal function depending on the energy. The connection between this representation for the potential scattering amplitude and the eikonal approximation in quantum field theory is discussed.

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. Barbashov B. M. et al., Phys. Lett. B,33 (1970) 419.

    Article  ADS  Google Scholar 

  2. Barbashov B. M. et al., Phys. Lett. B,33 (1970) 484.

    Article  ADS  Google Scholar 

  3. Matveev V. A. andTavkhelidze A. N.,Teor. Mat. Fiz.,9 (1971) 44.

    Article  Google Scholar 

  4. Nguyen Suan Han andNesterenko V. V.,Teor. Mat. Fiz.,24 (1975) 768.

    Article  Google Scholar 

  5. Nguyen Suan Han andPervushin V. N.,Teor. Mat. Fiz.,29 (1976) 1003.

    Article  Google Scholar 

  6. Barnashov B. M.,JEPT,48 (1965) 607.

    Google Scholar 

  7. Barnashov B. andVolkov M. K.,JEPT,50 (1966) 660.

    Google Scholar 

  8. ’t Hooft G.,Phys. Lett. B,198 (1987) 61.

    Article  ADS  Google Scholar 

  9. Amati D., Ciafaloni M. andVeneziano G.,Int. J. Mod. Phys. A,3 (1988) 1615.

    Article  ADS  Google Scholar 

  10. Amati D., Ciafaloni M. andVeneziano G.,Nucl. Phys. B,347 (1990) 550.

    Article  ADS  Google Scholar 

  11. Amati D., Ciafaloni M. andVeneziano G.,Phys. Lett. B,197 (1987) 81.

    Article  ADS  Google Scholar 

  12. Verlinde E. andVerlinde H.,Nucl. Phys. B,371 (1992) 246.

    Article  ADS  MathSciNet  Google Scholar 

  13. Kabat D. andOrtiz M.,Nucl. Phys. B,388 (1992) 570.

    Article  ADS  Google Scholar 

  14. Fabbrichesi M. et al., Nucl. Phys. B,419 (1994) 147.

    Article  ADS  Google Scholar 

  15. Muzinich I. andSoldate M.,Phys. Rev. D,37 (1988) 353.

    Article  ADS  Google Scholar 

  16. Lousto C. O. andSanchez N.,Phys. Lett.,232 (1989) 462.

    Article  Google Scholar 

  17. Arefdeva I. Ya., Viswanathan K. S. andVolovich I. V.,Nucl. Phys. B,452 (1995) 346.

    Article  ADS  Google Scholar 

  18. Kubota T. andTakashino H.,Prog. Theor. Phys.,94 (1995) 637.

    Article  ADS  Google Scholar 

  19. Kar S. andManharana J.,Int. J. Mod. Phys. A,10 (1995) 2733.

    Article  ADS  Google Scholar 

  20. Zeni M.,Class. Quantum Grav.,10 (1993) 905.

    Article  ADS  MathSciNet  Google Scholar 

  21. Hirschman I. I. andWidder D. V.,The Convolution Transform (Princeton University Press) 1955.

  22. Fock V. A.,The Theory of Space, Time and Gravitation (Pergamon Press) 1964.

  23. Fock V. A.,Z. Soviet Union,12 (1937) 474.

    Google Scholar 

  24. Feynman R. P.,Phys. Rev.,84 (1951) 108.

    Article  ADS  MathSciNet  Google Scholar 

  25. Nguyen Suan Han,JINR, P2-8570, Dubna, 1975.

  26. Maheshwari A.,Ann. Phys.,84 (1974) 474.

    Article  ADS  Google Scholar 

  27. Abarbanel H. andIzykson C.,Phys. Rev. Lett.,23 (1969) 53.

    Article  ADS  Google Scholar 

  28. Brezin E., Itzykson C. andZinn-Justin J.,Phys. Rev. D,1 (1970) 2349.

    Article  ADS  Google Scholar 

  29. Milekhin G. A. andFradkin E. S.,JEPT,45 (1963) 1926.

    Google Scholar 

  30. Glauber R. J.,Lect. Theor. Phys., Vol.1 (New York, N.Y.) 1959, p. 315.

    MathSciNet  Google Scholar 

  31. Pervushin V. N.,Teor. Mat. Fiz.,4 (1970) 28.

    Article  Google Scholar 

  32. Andreev I. A.,Zh. Eksp. Teor. Fiz.,58 (1970) 257.

    Google Scholar 

  33. Blokhintsev D. I. andBarbashov B. M.,Sov. Phys. Usp.,15 (1972) 193.

    Article  ADS  Google Scholar 

  34. Landau L. P. andLifschitz E. M.,The Field Theory (Nauka) 1973, p. 428.

  35. Mott N. F. andMassey H. S. W.,The Theory of Atomic Collisions, Chapt. 3 (Oxford) 1949.

Download references

Author information

Authors and Affiliations

  1. International Centre for Theoretical Physics, Trieste, Italy

    Nguyen Suan Han

  2. Physics Faculty, Phnom Penh University, Phnom Penh, Cambodia

    Eap Ponna

  3. Department of Theoretical Physics, Vietnam National University, P.O. Box 600, 10000, BoHo, Hanoi, Vietnam

    Nguyen Suan Han

Authors
  1. Nguyen Suan Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eap Ponna
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors of this paper have agreed to not receive the proofs for correction.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Han, N.S., Ponna, E. Straight-line path approximation for studying Planckian-energy scattering in quantum gravity. Il Nuovo Cimento A (1971-1996) 110, 459–473 (1997). https://doi.org/10.1007/BF03035893

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03035893

PACS 11.80

PACS 04.60

Search

Navigation