pair creation by a constant  electric
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

pair creation by a constant electric field PowerPoint PPT Presentation


  • 32 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

pair creation by a constant electric field

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Pair creation by a constant electric field

pair creation by a constant electric

field

N.B. Narozhny


Pair creation by a constant electric field

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


Pair creation by a constant electric field

is associated with the pair creation in the electric field


Pair creation by a constant electric field

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

The probability for vacuum to remain vacuum is

(R.Feynman)


Pair creation by a constant electric field

Let be the probability of pairs creation

Let


Pair creation by a constant electric field

actually


Pair creation by a constant electric field

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


Pair creation by a constant electric field

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


Pair creation by a constant electric field

The Feynman Green function (fermions)

Matrix element for pair production


Pair creation by a constant electric field

only this time interval effectively contributes to for given

classical turn point

formation length

and time


Pair creation by a constant electric field

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


Pair creation by a constant electric field

The probability for vacuum to remain vacuum

as it should be


Pair creation by a constant electric field

The total absolute probability of creation of

1 pair:

2 pairs:


Pair creation by a constant electric field

The average number of particles


Pair creation by a constant electric field

The total absolute probability of a single pair creation

and only if


Pair creation by a constant electric field

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


Pair creation by a constant electric field

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


Pair creation by a constant electric field

THANK YOU

FOR ATTENTION


  • Login