Pair creation in Feshbach-Villars formalism with two components

  • S. Haouat
  • L. Chetouani
theoretical physics


We have studied the behavior of the Feshbach-Villars equation (FV0) in comparison with the Klein-Gordon one (KG) in the problem of particle pair creation from the vacuum in an external electromagnetic field, considering two approaches: the Schwinger effective action method and the Bogoliubov transformation technique. In the first approach the vacuum to vacuum transition amplitude is calculated treating the FV0 field like a bosonic field. For the second approach, that uses canonical quantization, it is shown that the relative fields and their conjugate moments obey a commutation relation and not anticommutation one. The pair creation probability and the probability that the vacuum remains a vacuum calculated from the FV0 equation are, consequently, the same as those obtained from the KG one.


Electromagnetic Field Transition Amplitude Commutation Relation Effective Action Particle Acceleration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Gross, Relativistic quantum mechanics and field theory (Wiley-Interscience, New York 1993)Google Scholar
  2. 2.
    H. Feshbach, F. Villars, Rev. Mod. Phys. 30, 24 (1958)CrossRefGoogle Scholar
  3. 3.
    J.D. Bjorken, S.D. Drell, Relativistic quantum fields (McGraw Hill, New York 1965)Google Scholar
  4. 4.
    T. Boudjedaa, L. Chetouani, M. Merad, Il Nuovo Cimento 11, 1261 (1999); Chin. J. Phys. 6, 1020 (2000), Turk. J. Phys. 25, (2001)Google Scholar
  5. 5.
    M. Merad, L. Chetouani, A. Bounamés, Phys. Lett. A 267, 225 (2000)CrossRefGoogle Scholar
  6. 6.
    A. Bounamés, L. Chetouani, Phys. Lett. A 267, 225 (2000)CrossRefGoogle Scholar
  7. 7.
    B.A. Robson, S.H. Sutanto, Int. J. Theor. Phys. 40, 1491 (2001)CrossRefGoogle Scholar
  8. 8.
    J. Schwinger, Phys. Rev. 82, 664 (1951)CrossRefGoogle Scholar
  9. 9.
    W. Heisenberg, H. Euler, Z. Phys. 98, 714 (1936)CrossRefGoogle Scholar
  10. 10.
    B.R. Holstein, Am. J. Phys. 67, (Vol. 6) 499 (1998)Google Scholar
  11. 11.
    E.S. Fradkin, D.M. Gitman, S.M. Shvartsman, Quantum electrodynamics with unstable vacuum (Springer-Verlag, Berlin 1991)Google Scholar
  12. 12.
    A.I. Nikishov, hep-th/0111137Google Scholar
  13. 13.
    A.I. Nikishov, hep-th/0202024Google Scholar
  14. 14.
    S.P. Gavrilov, D.M. Gitman, hep-th/9603152 v1Google Scholar
  15. 15.
    A. Calogeracos, N. Dombey, Contemp. Phys. 40, 313 (1999)CrossRefGoogle Scholar
  16. 16.
    O. Klein, Z. Phys. 53, 157 (1929)CrossRefGoogle Scholar
  17. 17.
    I.S. Gradshteyn, I.M. Ryzhik, Table of integrals, series, and products (Academic Press, New York 1979)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  • S. Haouat
    • 1
  • L. Chetouani
    • 1
  1. 1.Département de Physique, Faculté de SciencesUniversité MentouriConstantineAlgérie

Personalised recommendations