Vacuum polarization, how does it work intuitively? I'm reading Penrose's "Road to reality" where he explains that around an electron there will spontaneously be generated e+/e- pairs which will then be separated from each other by the electron's charge and that this would reduce the actually "visible" charge of the electron which in fact (without this screening) would "in theory" be infinite. 
Now, here is my question: if I have an electron at position 0 a positron at position 1 and another electron at position 2 (the latter two being virtual and separated from each other by the influence of the e- at 0) like so 
    0  1  2  3   
    -  +  - 

then the charge seen from position 3 is actually slightly higher than that of 
the bare electron at 0. Namely the repulsion force seen by a negative test charge at 3 is 1/9-1/4+1 rather than just 1/9. Meaning the electron at 2 pushes harder than the positron at 1 is pulling. 
So, it looks as though the vacuum polarization increases the perceived charge rather than decreasing it. Can someone help me out of this conundrum?  
 A: Here's a slightly refined picture -- still very sketchy, but it gives the right sign. 
You need to account for the fact that there will be spherical shells of induced charge. In your example, you would have a shell of positive charge at $r = 1$ and a shell of negative charge at $r = 2$, and their effects will exactly cancel by the shell theorem. However, if you're between two shells, then only the inner one will have an effect (again by the shell theorem). Since the inner shell is positively charged, it counteracts the original negative charge.
A: The vacuum correction to the electron charge doesn't mainly come from pair creations (in fact, these terms do even cancel out) but from electron- or photon-loops etc. (the electron emits a photon and absorbs it again, the electron emits a photon which splits into an electron and a positron which annihilate again and are absorbed,...) or vertex corrections. There is also a shift of the electron mass because of that. To actually obtain the "theoretical" electron charge (or mass) is fairly difficult because all we can measure is the renormalized charged (which involves these extra terms, cancelling infinities,...). If you are interested in that topic, try a good QFT book or script, I can especially recommend Soff's script or https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf.
In the latter you can even find a little calculation of the charge correction terms and the renormalized magnetic moment of the electron.
