- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Schwinger pair production via instantons in strong electric fields

Sang Pyo Kim*

Don N. Page†

  • Department of Physics, Kunsan National University, Kunsan 573-701, Korea
  • Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1

  • CIAR Cosmology Program, Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1

  • *Electronic address: spkim@phys.ualberta.ca; sangkim@kunsan.ac.kr
  • †Electronic address: don@phys.ualberta.ca
PDF

Phys. Rev. D 65, 105002 – Published 19 April, 2002

DOI: https://doi.org/10.1103/PhysRevD.65.105002

Abstract

In the space-dependent gauge, each mode of the Klein-Gordon equation in a strong electric field takes the form of a time-independent Schrödinger equation with a potential barrier. We propose that the single instanton and multi-instantons of quantum tunneling may be related with the single-pair and multipair production of bosons and the relative probability for the no-pair production is determined by the total tunneling probability via instantons. In the case of a static uniform electric field, the instanton interpretation recovers exactly the well-known pair-production rate for bosons and, when the Pauli blocking is taken into account, it gives the correct fermion production rate. The instanton is used to calculate the pair-production rate even in an inhomogeneous electric field. Furthermore, the instanton interpretation confirms the fact that bosons and fermions cannot be produced by a static magnetic field only.

View figure in article

References (51)

  1. F. Sauter, Z. Phys. 69, 742 (1931).
  2. W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).
  3. J. Schwinger, Phys. Rev. 82, 664 (1951).
  4. V. Weisskopf, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 14, No. 6 (1936).
  5. B.S. DeWitt, Phys. Rep. 19, 295 (1975).
  6. W. Greiner, B. Múller, and J. Rafelski, Quantum Electrodynamics of Strong Fields (Springer, Berlin, 1985).
  7. L. Parker, Phys. Rev. Lett. 21, 562 (1968).
  8. L. Parker, Phys. Rev. 183, 1057 (1969).
  9. L. Parker, Phys. Rev. D 3, 346 (1971).
  10. E. Brezin and C. Itzykson, Phys. Rev. D 2, 1191 (1970).
  11. N.B. Narozhny and A.I. Nikishov, Sov. J. Nucl. Phys. 11, 596 (1970).
  12. V.S. Popov, Sov. Phys. JETP 34, 709 (1972).
  13. V.S. Popov, Sov. Phys. JETP 35, 659 (1972).
  14. J. Cornwall and G. Tiktopoulos, Phys. Rev. D 39, 334 (1989).
  15. A.B. Balantekin, J.E. Seger, and S.H. Fricke, Int. J. Mod. Phys. A 6, 695 (1991).
  16. Y. Kluger, J.M. Eisenberg, B. Svetitsky, F. Cooper, and E. Mottola, Phys. Rev. D 45, 4659 (1992).
  17. G. Dunne and T. Hall, Phys. Rev. D 58, 105022 (1998).
  18. T. Padmanabhan, Pramana 37, 179 (1991).
  19. R. Srinivasan and T. Padmanabhan, Phys. Rev. D 60, 024007 (1999).
  20. Cl. Gabriel and Ph. Spindel, Ann. Phys. (N.Y.) 284, 263 (2000).
  21. R.-C. Wang and C.-Y. Wong, Phys. Rev. D 38, 348 (1988).
  22. C. Martin and D. Vautherin, Phys. Rev. D 38, 3593 (1988).
  23. C. Martin and D. Vautherin, Phys. Rev. D 40, 1667 (1989).
  24. C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
  25. A. Casher, H. Neuberger, and S. Nussinov, Phys. Rev. D 20, 179 (1979).
  26. H. Neuberger, Phys. Rev. D 20, 2936 (1979).
  27. A. Casher, H. Neuberger, and S. Nussinov, Phys. Rev. D 21, 1966 (1980).
  28. A.I. Nikishov, Nucl. Phys. B21, 346 (1970).
  29. A. Hansen and F. Ravndal, Phys. Scr. 23, 1033 (1981).
  30. O. Klein, Z. Phys. 53, 157 (1929).
  31. F. Hund, Z. Phys. 117, 1 (1940).
  32. C.R. Stephens, Ann. Phys. (N.Y.) 193, 255 (1989).
  33. R. Brout, R. Parentani, and Ph. Spindel, Nucl. Phys. B353, 209 (1991).
  34. R. Brout, S. Massar, R. Parentani, and Ph. Spindel, Phys. Rep. 260, 329 (1995).
  35. R. Parentani and S. Massar, Phys. Rev. D 55, 3603 (1997).
  36. G. Preparata, R. Ruffini, and S.-S. Xue, Astron. Astrophys. 338, L87 (1998).
  37. R. Ruffini, J.D. Salmonson, J.R. Wilson, and S.-S. Xue, Astron. Astrophys. 350, 334 (1999).
  38. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
  39. S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985).
  40. V.P. Gusynin and I.A. Shovkovy, J. Math. Phys. 40, 5406 (1999).
  41. A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev, Integrals and Series (Gordon and Breach, Amsterdam, 1986), Vol. 1.
  42. W. Dittrich, W.-Y. Tsai, and K.-H. Zimmermann, Phys. Rev. D 19, 2929 (1979).
  43. J.S. Heyl and L. Hernquist, Phys. Rev. D 55, 2449 (1997).
  44. R. Soldati and L. Sorbo, Phys. Lett. B 426, 82 (1998).
  45. J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Addison-Wesley, Reading, MA, 1955).
  46. N. Fröman and P.O. Fröman, Nucl. Phys. A147, 606 (1970).
  47. N. Fröman and P. O. Fröman, Phase-Integral Method (Springer, New York, 1996).
  48. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I (Springer, New York, 1999).
  49. L. Sriramkumar and T. Padmanabhan, Phys. Rev. D 54, 7599 (1996).
  50. G.V. Dunne and T.M. Hall, Phys. Lett. B 419, 322 (1998).
  51. G.V. Dunne and T.M. Hall, Phys. Rev. D 60, 065002 (1999).

Outline

Information

Phys. Rev. D 65, 105002– Published 19 April, 2002
  • Received 9 May 2000

© 2002 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation