Classical Version of Vacuum Polarization

[ApplePion]

The vacuum polarization result in QED seems to always be written in a "QED form". I would be interested in seeing it in an old-fashioned classical physics form.

Without vacuum polarization the electric potential in a region containing a point charge is of course Q/r. So if the vacuum polarization is included the potential must be of some form Q f(r) where f(r) is no longer 1/r. So what specifically would f(r) be?

Thanks.

 

[sancharsharma]

But classical physics doesn't predict any vacuum polarisation...

So how can we find a function which is non existent??

i failed to understand your question probably...

 

[ApplePion]

Yes, I realize that classical physics does not fully predict the phenomenon, but the pairs whose creation was predicted by QED do produce electric fields in accordance with the rules for electric field generation. More important though is that one should be able to in principle do an actual physical experiment--take a point charge and actually measure the electric field around it. Doing the experiment one would get actual numerical data to construct the field as a function of position. What you would get would deviate from the inverse distance squared non-QED function. So what I want to know is what the actual function would be. There IS some function, and it should be expressable in the form E = g(r), where g(r) is a normal function!

 

[granpa]

The vacuum polarization result in QED seems to always be written in a "QED form". I would be interested in seeing it in an old-fashioned classical physics form.

Without vacuum polarization the electric potential in a region containing a point charge is of course Q/r. So if the vacuum polarization is included the potential must be of some form Q f(r) where f(r) is no longer 1/r. So what specifically would f(r) be?

Thanks.

I don't understand.
Polarization just masks some of the charge.
the potential equation should be the same.
Shouldnt it?

 

[Bob S]

The basic equation for the vacuum polarization correction potential was first derived by Uehling in Phys Rev 48, page 55 (1935). The correction (shielding of the bare charge) extends out to about 1 electron Compton wavelength, so it is a large (often over 1%) correction to atomic binding energies in pionic and muonic atoms.

The Uehling integral is rewritten in a more useful integrable form in Appendix B of Shafer "Pion Mass Measurement..." Phys Rev 163 page 1451 (1967).

Bob S

 

[ApplePion]

Excellent answer, Bob S.

Thanks.