- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

(F, G)-summed form of the QED effective action

Jose Navarro-Salas* and Silvia Pla†

  • Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC. Facultad de Fisica, Universidad de Valencia, Burjassot-46100, Valencia, Spain

  • *jnavarro@ific.uv.es
  • †silvia.pla@uv.es
PDF

Phys. Rev. D 103, L081702 – Published 21 April, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.L081702

Abstract

We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants F=14FμνFμν(x), G=14F˜μνFμν(x), including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide strong evidence for this conjecture, which is proved to sixth order in the proper time. Furthermore, and as a byproduct, we generate some solvable electromagnetic backgrounds. We also discuss the implications for a generalization of the Schwinger formula for pair production induced by nonconstant electric fields. Finally, we briefly outline the extension of these results in the presence of gravity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (47)

  1. W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).
  2. G. Dunne, in From Fields to Strings: Circumnavigating Theoretical Physics, edited by M. Shifman, A. Vainshtein, and J. Wheater (World Scientific, 2005), pp. 445–522, 10.1142/9789812775344_0014; arXiv:hep-th/0406216.
  3. M. D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge University Press, Cambridge, England, 2014).
  4. G. V. Dunne, Int. J. Mod. Phys. A 27, 1260004 (2012); F. Karbstein, Particles 3, 39 (2020).
  5. V. Weisskopf, Kong. Dan. Vid. Sel. Mat. Fys. Med. 14N6, 1 (1936), https://inspirehep.net/literature/1303283.
  6. J. Schwinger, Phys. Rev. 82, 664 (1951).
  7. V. S. Vanyashin and M. V. Terent’ev, Sov. Phys. JETP 21, 375 (1965), http://www.jetp.ac.ru/cgi-bin/dn/e_021_02_0375.pdf.
  8. G. V. Dunne, Eur. Phys. J. D 55, 327 (2009).
  9. L. Parker, Phys. Rev. Lett. 21, 562 (1968); Phys. Rev. 183, 1057 (1969).
  10. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).
  11. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
  12. S. A. Fulling, Aspects of Quantum Field Theory in Curved Space-Time (Cambridge University Press, Cambridge, England, 1989).
  13. L. Parker and D. J. Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity (Cambridge University Press, Cambridge, England, 2009).
  14. D. V. Vassilevich, Phys. Rep. 388, 279 (2003).
  15. B. S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965).
  16. P. B. Gilkey, J. Diff. Geom. 10, 601 (1975).
  17. J. D. Bekenstein and L. Parker, Phys. Rev. D 23, 2850 (1981).
  18. L. Parker and D. J. Toms, Phys. Rev. D 31, 953 (1985).
  19. I. Jack and L. Parker, Phys. Rev. D 31, 2439 (1985).
  20. A. Ferreiro, J. Navarro-Salas, and S. Pla, Phys. Rev. D 101, 105011 (2020).
  21. L. Parker and A. Raval, Phys. Rev. D 60, 063512 (1999).
  22. L. Parker and A. Raval, Phys. Rev. D 62, 083503 (2000).
  23. L. Parker and D. A. T. Vanzella, Phys. Rev. D 69, 104009 (2004).
  24. R. R. Caldwell, W. Komp, L. Parker, and D. A. T. Wanzella, Phys. Rev. D 73, 023513 (2006).
  25. E. Di Valentino, E. V. Linder, and A. Melchiorri, Phys. Rev. D 97, 043528 (2018).
  26. T. Markkanen, S. Nurmi, A. Rajantie, and S. Stopyr, J. High Energy Phys. 06 (2018) 040.
  27. E. V. Castro, A. Flachi, P. Ribeiro, and V. Vitagliano, Phys. Rev. Lett. 121, 221601 (2018).
  28. O. Czerwinska, Z. Lalak, and L. Nakonieczny, J. High Energy Phys. 11 (2015) 207.
  29. E. Calzetta, I. Jack, and L. Parker, Phys. Rev. Lett. 55, 1241 (1985).
  30. D. Fliegner, P. Haberl, M. G. Schmidt, and C. Schubert, Ann. Phys. (N.Y.) 264, 51 (1998).
  31. D. Fliegner, M. G. Schmidt, and C. Schubert, Nucl. Instrum. Methods Phys. Res., Sect. A 389, 374 (1997).
  32. D. Fliegner, M. G. Schmidt, and C. Schubert, Z. Phys. C 64, 111 (1994).
  33. M. Reuter, M. G. Schmidt, and C. Schubert, Ann. Phys. (N.Y.) 259, 313 (1997).
  34. M. G. Schmidt and C. Schubert, Phys. Lett. B 318, 438 (1993).
  35. Z. Bern and D. A. Kosower, Phys. Rev. Lett. 66, 1669 (1991).
  36. U. Müller, New Computing Techniques in Physics Research IV (World Scientific, Singapore, 1996), p. 193; DESY-96-154, arXiv:hep-th/9701124.
  37. V. P. Gusynin and I. A. Shovkovy, J. Math. Phys. (N.Y.) 40, 5406 (1999).
  38. S. Pla, I. M. Newsome, R. S. Link, P. R. Anderson, and J. Navarro-Salas, arXiv:2010.09811 [Phys. Rev. D (to be published)].
  39. H. M. Fried and R. P. Woodard, Phys. Lett. B 524, 233 (2002).
  40. T. N. Tomaras, N. C. Tsamis, and R. P. Woodard, Phys. Rev. D 62, 125005 (2000).
  41. A. Ilderton, J. High Energy Phys. 09 (2014) 166.
  42. I. G. Avramidi and G. Fucci, Commun. Math. Phys. 291, 543 (2009).
  43. G. Fucci and I. G. Avramidi, in 9th Conference on Quantum Field Theory under the Influence of External Conditions (QFEXT 09), pp. 485–491 [arXiv:0911.1099].
  44. I. T. Drummond and S. J. Hathrell, Phys. Rev. D 22, 343 (1980).
  45. F. Bastianelli, J. M. Davila, and C. Schubert, J. High Energy Phys. 03 (2009) 086.
  46. C. de Rham and A. J. Tolley, Phys. Rev. D 102, 084048 (2020).
  47. J. M. Martín-García, xact: Efficient tensor computer algebra for the Wolfram language, https://www.xAct.es; R. Mertig, M. Böhm, and A. Denner, Comput. Phys. Commun. 64, 345 (1991).

Outline

Information

Phys. Rev. D 103, L081702– Published 21 April, 2021
  • Received 4 December 2020
  • Accepted 11 March 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation