QED vs Point Charge of the Electron

Buckeye

If the electron is a point charge, then its' charge to mass ratio approaches infinity. How does the Standard Model (QED) deal with this?

marlon

RENORMALIZATION

regards
marlon

Theoretician

Excuse my ignorance but how so?

Physics Monkey

I would assume Buckeye is referring to the fact that a point particle has a divergent electromagnetic self energy. What has not been mentioned is that the charge of the electron also diverges. As marlon said, both these divergences are dealt with by first acknowledging our ignorance of the high energy physics and then by renormalizing both parameters at each order in perturbation theory. The predictive power of the theory is restored.

Rade

Question...does this then mean that, if we had knowledge (not ignorance) of the physics, we would do away with renormalization ? And, if so, what would replace renormalization ?

Buckeye

If we treat the electron as a charge with a finite size, do we need to renormalize?

vanesch

Yes. The infinity comes about of our ignorance of the structure of the electron. That's why we make it a *point* particle. This comes down to saying that an electron can interact, as a WHOLE, and transmit arbitrary high momenta. It is the integration over these arbitrary high momenta which make quantities diverge in QFT. If the electron has a structure (say, a string or something else) then of course it will not be able to transmit higher momenta (= short wavelengths) than the size of its structure ; at higher momenta, we would start to see the effects of its structure (like happens for instance with a proton: you cannot have very high momentum transfer to a *proton*, because when you try to do so, you break up the proton: that's called deep inelastic scattering). What we do in renormalization, is to propose an arbitrary scale at which we cut off the momentum transfer to the electron (as if it had structure at this scale). It then turns out, in renormalizable theories, that the low-energy behaviour becomes independent of the exact value of this cutoff scale, as long as it is high enough. So we can just as well take its limit to infinity.
What happens then is that the *relationship* between low energy quantities remains unchanged.
In non-renormalizable theories, this doesn't happen: we depend for the low energy behaviour crucially on the details of the cutoff (of the arbitrary structure we introduced).

marlon

Check out THIS if you wanna know more on renormalization.

Trust me, the source is reliable

regards
marlon

selfAdjoint

Reliable? Famous perhaps, but also maybe cranky? It doesn't follow because somebody made a wonderful discovery back when, that he is today a reliable guide on controversial issues. Recall Dirac and his later life adventures.

marlon

I was not talking in general terms here. In the case of Gerardus 't Hooft the situation is very clear. Well, perhaps not his visions on string theory but even with those i agree with him. But, this does not change much since we are talking about QED renormalization here

regards
marlon

Buckeye

I read 't Hooft's Nobel lecture and understand most of it. Now I'm wondering if QED moved in this direction because Dirac's theory depends on the electron and other particles to act or be point particles.
Yes, No or Option C?