Virtual shell around a charged particle?

[nomadreid]

In quantum renormalization, one distinguishes between the (unobservable) bare electron and the observable properties. The justifications that I can find for the procedure seem to rest purely on mathematical and empirical grounds: the methods are in line with a consistent mathematical theory, it can survive different measurement scaling, and it gives the right answers. However, long, long ago (so long ago that I cannot find a reference to this), I read an attempt to justify the methods which said that the bare electron increased the probability of virtual positive particles forming (and disappearing) around it, so that the on-the-average positive shell reduced the charge of the bare electron when we measure it outside of this shell. The fact that I have not read this elegant explanation recently leads me to suspect that it has been discredited, despite its charm. (Of course, I don't know how this would be adapted for gravitation, but probably no one else does as well, so that's OK, innit?) Has it? If it hasn't, why doesn't it appear? If it has, is there any other known physical reason for the individual steps of methods of renormalization to work?

 

[vanhees71]

I don't know to which reference you refer either, but isn't this just the standard interpretation of quantum-fluctuation effects on a point charge. If you calculate the self-energy of the photon and apply the linear-response-theoretical formalism to a point charge at rest, you obtain an electrostatic field which is a Coulomb field screened by the quantum fluctuations. In the most simple approximation (one-loop level) these fluctuations are given by virtual electron-positron-pair creation/destruction processes. This interpretation of the photon-self energy is also the reason why this radiative correction is named the vacuum-polarization effect.

 

[nomadreid]

Thanks, vanhees71. Ah, OK, so my memory serves me correctly. Therefore I should look for the vacuum polarization effect in discussions of renormalization. Let's take the Wikipedia article on polarization as an example. On one side the vacuum polarization effect is quoted as a cause of a problematic divergence, that is something that counter-terms are needed to cancel out in the taking of the limits, and on the other side it is mentioned in a drawing that "vacuum polarization" is also known as "charge screening"; this latter remark would seem to be an implicit suggestion that it contributes to the counter-terms, but this is never explicitly stated or developed in the text. Indeed, in the articles on renormalization, either the contribution of quantum fluctuations to the counter-terms is not explicitly worked out, or I am overlooking it.

 

[vanhees71]

A pretty good explanation of the meaning of vacuum polarization (and the other radiative corrections QED) is given in

Peskin, Schroeder, An Introduction to Quantum Field Theory

 

[nomadreid]

Thanks for the recommendation. I shall look into getting it, although I am presently in a country without bookstores or public libraries having such books.