Sunday, November 11, 2007

Renormalization

Today, I want to write about a serious complication that occurs in two particle interactions.


The above depicted gluon exchange is not as simple as it might seem, because virtual particles make contributions to the process


The troublesome thing about these contributions is that there are in principle arbitrarily many of them with arbitrarily high energy


You can easily convince yourself that this process is IQ divergent. One therefore sums up all the virtual contributions, and redefines the initial propagation of exchange particles


This is called renormalization.

(Larger picture)

28 comments:

  1. How would this work for same-sex particles?

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  2. Hi Anonymous,

    ff: multiply HE-vertices with s
    mm: divide SHE-vertices by s

    I haven't worked with that model, so I'm not sure whether the additional symmetry factor affects cross-sections.

    Hi Mars,

    Thanks :-) Say hello to Venus,

    B.

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  3. Dear Bee,

    that's great :-)

    Best, Stefan

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  4. This is cute, and remember that physics is different for "dressed" than for "undressed" particles!
    But what about "real" renormalization: Is it a reasonable theory, or a contrived hack? Even if you take polarization of the vacuum into account, what is the integral of field energy around an electron down to the alleged "point" center, or to a string of some kind? I still don't see how it could be less than the mass of the electron, since field energy density varies as intensity squared and there's a "long way to go."

    But if the integrated field mass equivalent is more than m_e, then there's a contradiction. Don't say, that's just a classical problem, because the same issue should be relevant - only the handling of it would be different.

    I've asked before in different places for a graph of electric field around a "dressed" electron as deviation from simple 1/r^2 as would be classically for a charge with distant flux of that charge. I have yet to see it referenced.

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  5. Hi Neil,

    well, I assume you can read what the textbooks say, so I interpret your question as asking for my opinion. I think renormalization is a doable but ugly way to deal with our lack of knowledge about what 'really' happens at Planckian energies.

    Even in classical EM, the potential is defined only up to a constant, and you can only measure potential differences.

    Best,

    B.

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  6. Thanks, Bee.

    One point to clarify if you have a minute: you spoke of potential, but IIUC the field energy density is based on field strength, and is therefore an absolute ('tho may be hard to define in the regions close to the electron's source.)

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  7. What I was actually talking about in my above comment is renormalization : :, normal ordering of operators. What I was talking about in the post is renormalization of the bare masses/couplings.

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  8. I thought I had typed to go to asymptotia, and I was wondering why Clifford was tryng Bee-ish jokes :) .

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  9. glad I didn't add the line about asymptotic freedom that I had in mind - it would have confused you even more ;-)

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  10. Confusion , (and the subsequent unravelling) are useful :). So, I would love to hear the part about asymptotic freedom.

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  11. OMG yes. :)

    Incidentally, I just learned in my E&M class if you treat a point charge distribution as a continuous charge distribution, its total energy seems to be infinite! Now the idea of renormalization seems a lot less shady to me...

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  12. Oh man, this is totally going on the wall outside my door. Most excellent!

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  13. I think that you need more than two sexes to make these diagrams convergent.

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  14. When she likes him, and he likes her, it is a Yes-matrix element.

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  15. I think that there ought to be a (1/2!)^2 symmetry factor since there are identical particles in the initial & final states; for same-sex particles the graphs ought to be the same unless they are all in the final or all in the initial states, which you could get by crossing, e.g. one chick having a crush on three other chicks simultaneously.

    If the lesbian 1 on 3 experiment is ever carried out, it could be funded by having a subscription services to the video footage on the internet, thus avoiding the tiresome process of filling in grant application forms.

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  16. Now I don't know what Gross and Wilczek would say about this picture of renormalization, but I'll say that asymptotic freedom could bring much needed heat (and spice) to it!

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  17. Hi Anonymous,

    well, it was only one sentence saying the strong interaction is asymptotically free. it lead my thoughts running towards confinement however, and I found I shouldn't overstretch it. It's kind of interesting though, I've referred earlier to communication as 'gluons' and occasionally it seems to me that the stronger the coupling and the denser the medium, the less confinement. That is to say, it seems to be much more accepted to stay single today than, say, 100 years ago, and families dissolve into social networks. Where's the hadronization gone? Best,

    B.

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  18. When states cross in chemistry they instead split and separate, or Jahn-Teller distortion diddles the outcome. This models why academic chemistry labs are well-staffed on Friday and Saturday nights.

    If NSF won't fund this reasrch, NIH will get all jiggy wit it.

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  19. "He likes her" and "She likes him" often leads to super-something.

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  20. sorry, our server is down, so the pics are gone. hopefully back up and running later today.

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  21. our server is down, so the pics are gone. hopefully back up and running later today.

    This seems to be quite a severe problem - not only the web services are affected, but email and remote access doesn't work either. And usually, the problem is fixed within a few hours. Now, I fear that the outage will persist at least until tomorrow, i.e. for more than 12 hours...

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  22. Aaaahhh!! Here we go! One Googol of thanks to the never-sleeping system admin back at the ITP in Frankfurt :-)

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  23. Just as well both particles thought they liked one another. What if it was a case of unrequited love?
    :-(

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  24. Nice

    As for unrequited love - some sort of no-go theorem perhaps?

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  25. ahaha so funny and cute!

    Amazing post! Actually all your humor posts are awesome! Just met your blog and I can't stop reading it!

    Best,
    Fernanda..

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