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pair creation by a constant electric field

pair creation by a constant electric field. N.B. Narozhny. W. Heisenberg, H. Euler , Z. Phys. 98 , 714 (1936). linear Maxwell equations. em fields (photons) do not interact. nonlinear correction to Maxwell equations. photons do interact!. elastic photon-photon scattering.

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pair creation by a constant electric field

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  1. pair creation by a constant electric field N.B. Narozhny

  2. W. Heisenberg, H. Euler, Z. Phys. 98, 714 (1936) linear Maxwell equations em fields (photons) do not interact nonlinear correction to Maxwell equations photons do interact! elastic photon-photon scattering

  3. is associated with the pair creation in the electric field

  4. J. Schwinger, Phys. Rev., 82, 664 (1951) The probability for vacuum to remain vacuum is (R.Feynman)

  5. Let be the probability of pairs creation Let

  6. actually

  7. Probability of pair creation N.Narozhny, A.Nikishov, Yad.Fiz, 11, 1072(1970) 4-potential for a constant electric field: Solutions of a wave equation cannot be characterized by a definite sign of frequency

  8. There exists a complete and orthonormal set of solutions Describes particles and antiparticles at There exists another set of solutions Describes particles and antiparticles at There exist Bogolyubov relations between the sets

  9. The Feynman Green function (fermions) Matrix element for pair production

  10. only this time interval effectively contributes to for given classical turn point formation length and time

  11. The relative probability of pair creation with quantum numbers The absolute probability of pair creation with quantum numbers the probability that pair with quantum numbers was not created

  12. The probability for vacuum to remain vacuum as it should be

  13. The total absolute probability of creation of 1 pair: 2 pairs:

  14. The average number of particles

  15. The total absolute probability of a single pair creation and only if

  16. Invariant characteristics of electromagnetic field 1. Pairs can be created in an electromagnetic field with 2. Pairs cannot be created in an electromagnetic field with For case 1 we can always find a reference frame with For case 2 we can always find a reference frame with J.Schwinger (1951): Pairs can be created in an electromagnetic field with independently of If , we can always find a reference frame with Pairs can be created if

  17. For arbitrary static and uniform em field with If the field is not static and uniform but and are space and time scale of variation of the field

  18. THANK YOU FOR ATTENTION

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