Skip to main content
SpringerLink
Log in

The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (spinless case)

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

Summary

Starting with a pair of integrodifferential Bethe-Salpeter equations for two spinless particles interacting mutually and with an external static potential, we obtain a pair of compatible and separable coupled Klein-Gordon equations, between which the unwanted relative time variable can be easily eliminated. The method we use is a generalization of that proposed by Sazdijan for the two-particle problem, and the resulting equations are a generalization of the well-known Droz-Vincent-Todorov-Komar equations of relativistic quantum mechanics. We examine the instantaneous approximation and we test our methods in a simple case (Bethe-Salpeter kernel given by a single scalar particle exchange graph).

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. P. Droz-Vincent:Rep. Math. Phys.,8, 79 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  2. I. T. Todorov: Report JINR E2-10125 (Dubna, 1976), unpublished;Ann. Inst. Henri Poincaré A,28, 207 (1978).

  3. A. Komar:Phys. Rev. D,18, 1881, 1887 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  4. H. Sazdjian:Phys. Rev. D,33, 3401, 3425, 3435 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  5. H. Sazdjian:Lett. Math. Phys.,5, 319 (1981);Ann. Phys. (N.Y.),136, 136 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  6. S. I. Bidikov andI. T. Todorov:Lett. Math. Phys.,5, 461 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  7. F. Rohrlich:Phys. Rev. D,23, 1305 (1981);T. Biswas andF. Rohrlich:Lett. Math. Phys.,6, 325 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  8. J. Bijtebier:Nuovo Cimento A,100, 91 (1988);103, 317 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  9. J. Bijtebier:Nuovo Cimento A,102, 1285 (1989).

    Article  Google Scholar 

  10. J. Bijtebier:Nuovo Cimento A,103, 639, 669 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  11. H. Sazdjian:Phys. Lett. B,208, 470 (1988);Ann. Phys. (N.Y.),191, 52 (1989).

    Article  ADS  Google Scholar 

  12. P. Droz-Vincent:Ann. Inst. Henri Poincaré,50, 187 (1989);Phys. Lett. A,139, 9 (1989),147, 406 (1990).

    MathSciNet  Google Scholar 

  13. H. Sazdjian:J. Math. Phys. (N.Y.),28, 2618 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  14. H. W. Crater andP. Van Alstine:Phys. Rev. D,37, 1982 (1988).

    Article  ADS  Google Scholar 

  15. I. T. Todorov:Phys. Rev. D,3, 2351 (1971).

    Article  ADS  Google Scholar 

  16. S. S. Schweber:An Introduction to Relativistic Quantum Field Theory (Harper and Row, New York, N.Y., 1961).

    MATH  Google Scholar 

  17. G. S. Adkins: inAIP Conf. Proc.,189 (New York, 1989).

  18. H. A. Bethe andE. E. Salpeter:Quantum Mechanics of One-and Two-Electron Atoms (Plenum Publishing Corporation, New York, N.Y., 1977).

    Book  MATH  Google Scholar 

  19. J. Bijtebier andJ. Broekaert:The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (two-fermion case), preprint VUB/TENA/91/04, to be published inNuovo Cimento A.

  20. M. H. Mittleman:Phys. Rev. A,39, 1 (1989).

    Article  ADS  Google Scholar 

  21. J. Sucher:Phys. Rev. Lett.,55, 1033 (1985).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretische Natuurkunde, Fakulteit der Wetenschappen, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, Belgium

    J. Bijtebier & J. Broekaert

  2. Vorsers bij het Nationaal Fonds voor Wetenschappelijk Onderzoek, Belgium

    J. Bijtebier & J. Broekaert

Authors
  1. J. Bijtebier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Broekaert
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bijtebier, J., Broekaert, J. The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (spinless case). Nuov Cim A 105, 351–369 (1992). https://doi.org/10.1007/BF02730640

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02730640

PACS

Search

Navigation