Renormalization as a dielectric

  • Thread starter RedX
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Can renormalization of QED really be interpreted as a dielectric shielding of the vacuum by electron/positron pairs that appear and disappear out of the vacuum?

I understand that's what the Feynman diagram for the QED vertex suggests, since it's the internal fermion lines that interact with a photon (forming a triangle to which you can attach 3 external lines) that gives you the correction to the tree vertex, making it finite.

But I thought virtual particles were fictitious in that they are mathematical constructs and not really real particles. Presumably virtual particles wouldn't exist if one could figure out a way to integrate exponentials of terms higher than quadratic, so that there would be no need for perturbation theory to evaluate such an integral!

Can the analogy be pushed farther: can one define a dielectric constant of the vacuum, and speak of the electric polarization of the vacuum? What about the relations that you get from classical physics, that the bound charge is the divergence of the polarization vector P:

[tex]\rho_b=-\nabla \cdot P [/tex]

or that the polarization current is:

[tex]j_p=\frac{\partial P}{\partial t} [/tex]

It seems to me that one should be able to define these concepts, or else what's the point in calling the vacuum a dielectric? Yet I've never seen it in textbooks.
 

Bill_K

Science Advisor
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Take a look at Weinberg's book, Vol I Sect 11.2, which is devoted to calculating and interpreting the vacuum polarization.
 

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