Skip to main content
SpringerLink
Log in

Peculiarities of Pair Creation by a Peak Electric Field

  • Published:
Russian Physics Journal Aims and scope

An Erratum to this article was published on 07 August 2017

This article has been updated

Exact, numerical, and asymptotic calculations concerning the vacuum instability by the so-called peak electric field are explored in detail. Peculiarities discussed in this article are complementary to those published recently by us in Eur. Phys. J. C, 76, p. 447 (2016), in which the effect was studied in the framework of QED with t -electric potential steps. To discuss features beyond the asymptotic regime, we present numerical details of exact and asymptotic expressions inherent to the peak field and discuss differential and total quantities. The results show wider distributions, with respect to the longitudinal momentum, as the phases k1 and k2 of the electric field decrease and larger distributions as the amplitude E increases. Moreover, the total density of pairs created decreases as k1 and k2 increase, its dependence being proportional to \( {k}_1^{-1} \) and \( {k}_2^{-1} \). The latter result is more accurate as k1 and k2 decrease and confirms, in particular, our asymptotic estimates obtained previously.

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

Change history

  • 07 August 2017

    An erratum to this article has been published.

References

  1. O. Klein, Z. Phys., 53, 157 (1929).

    Article  ADS  Google Scholar 

  2. F. Sauter, Z. Phys., 69, 742; 73, 547 (1931).

  3. W. Heisenberg and H. Euler, Z. Phys., 98, 714 (1936).

    Article  ADS  Google Scholar 

  4. F. Hund, Z. Phys., 117, 1 (1940).

    Article  ADS  Google Scholar 

  5. J. Schwinger, Phys. Rev., 82, 664 (1951).

    Article  ADS  Google Scholar 

  6. W. H. Furry, Phys. Rev., 81, 115 (1951).

    Article  ADS  MathSciNet  Google Scholar 

  7. A. I. Nikishov, Zh. Eksp. Teor. Fiz., 57, No. 4, 1210–12160 (1970).

    Google Scholar 

  8. N. B. Narozhnyi and A. I. Nikishov, Yad. Fiz., 11, 1072 (1970).

    Google Scholar 

  9. A. I. Nikishov, Trudy FIAN SSSR, 111, 153–271 (1979).

    Google Scholar 

  10. A. I. Nikishov, Nucl. Phys. B, 21, 346 (1970).

    Article  ADS  Google Scholar 

  11. A. I. Nikishov, Yad. Fiz., 67, No. 8, 1503-1511 (2004); arXiv:hep-th/0111137.

  12. A. I. Nikishov and V. I. Ritus, Zh. Eksp. Teor. Fiz., 46, No. 2, 776–796 (1964); No. 5, 1768–1781 (1964).

  13. N. B. Narozhnyi and A. I. Nikishov, Teor. Mat. Fiz., 26, No. 1, 16–34 (1976).

    Article  Google Scholar 

  14. E. Brezin and C. Itzykson, Phys. Rev. D, 2, 1191 (1970).

    Article  ADS  Google Scholar 

  15. V. S. Popov, Zh. Eksp. Teor. Fiz., 62, No. 4, 1248–1262 (1972).

    Google Scholar 

  16. D. M. Gitman, J. Phys. A, 10, 2007–2020 (1977).

    Google Scholar 

  17. E. S. Fradkin and D. M. Gitman, Fortschr. Phys., 29, 381–411 (1981).

    Article  Google Scholar 

  18. E. S. Fradkin, D. M. Gitman, and S. M. Shvartsman, Quantum Electrodynamics with Unstable Vacuum, Springer, Berlin (1991).

    Book  Google Scholar 

  19. W. Greiner, B. Müller, and J. Rafelsky, Quantum Electrodynamics of Strong Fields, Springer, Berlin (1985).

    Book  Google Scholar 

  20. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge University Press, Cambridge (1982).

    Book  MATH  Google Scholar 

  21. A. A. Grib, S. G. Mamayev, V. M. Mostepanenko, Vacuum Quantum Effects in Strong Fields, Friedman Laboratory Publishing, Saint Petersburg (1994).

    Google Scholar 

  22. S. P. Gavrilov and D. M. Gitman, Phys. Rev. D, 53, 7162–7175 (1996).

    Article  ADS  Google Scholar 

  23. T. C. Adorno, S. P. Gavrilov, and D. M. Gitman, arXiv:1512.01288.

  24. R. Ruffini, G. Vereshchagin, and S. Xue, Phys. Rep., 487, 1–140 (2010).

    Article  ADS  Google Scholar 

  25. F. Gelis and N. Tanji, Prog. Part. Nucl. Phys., 87, 1–49 (2016).

    Article  ADS  Google Scholar 

  26. T. C. Adorno, S. P. Gavrilov, and D. M. Gitman, Eur. Phys. J. C, 76, 447 (1–15) (2016).

  27. T. C. Adorno, S. P. Gavrilov, and D. M. Gitman, Physica Scripta, 90, 074005 (1–8) (2015).

  28. Higher Transcendental Functions (Bateman Manuscript Project), Vols. 1 and 2, A. Erdélyi et al., eds., McGraw-Hill, New York (1953).

  29. NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, 2015-08-07 DLMF Update; Version 1.0.10.

  30. S. S. Schweber, An Introduction to Relativistic Quantum Fields, Dover Publications, Mineola, New York (2005).

    MATH  Google Scholar 

  31. I. A. Aleksandrov, G. Plunien, and V. M. Shabaev, Phys. Rev. D, 94, 065024 (2016).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Research Tomsk State University, Tomsk, Russia

    T. C. Adorno, S. P. Gavrilov & D. M. Gitman

  2. Herzen State Pedagogical University of Russia, Saint Petersburg, Russia

    S. P. Gavrilov

  3. P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia

    D. M. Gitman

  4. Institute of Physics of the University of São Paolo, São Paolo, Brazil

    D. M. Gitman & R. Ferreira

Authors
  1. T. C. Adorno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. P. Gavrilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. M. Gitman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. C. Adorno.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 37–45, March, 2017.

An erratum to this article is available at https://doi.org/10.1007/s11182-017-1133-4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Adorno, T.C., Gavrilov, S.P., Gitman, D.M. et al. Peculiarities of Pair Creation by a Peak Electric Field. Russ Phys J 60, 417–426 (2017). https://doi.org/10.1007/s11182-017-1090-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-017-1090-y

Keywords

Search

Navigation