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Renormalization Group for dummies 
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#19
Feb2112, 06:30 PM

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So you are saying that Renormalization Group concepts and regulator thing are also used in biology, economics, finance and not just in QFT? So in the calculations in biology. The coupling constant equivalent can become infinite in the second term but if one makes a cutoff at first term. it is finite? 


#20
Feb2112, 06:35 PM

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#21
Feb2112, 06:41 PM

P: 381




#22
Feb2112, 07:03 PM

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#23
Feb2112, 07:10 PM

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Less facetiously, the philosophy of the central limit theorem is like the renormalization group. Take the heights of people. That's due to hundreds of genes, whose interactions we hardly understand. Yet when you plot a distribution of heights of populations, very often you get a Gaussian distribution characterized fully by two parameters: mean and variance. So if you are looking coarsely on a population level, you don't need the theory of all the genes with hundreds of parameters  you just need the Gaussian distribution with two parameters. Here the Gaussian distribution is derived using the renormalization group: http://www.math.princeton.edu/facult...gorovLec07.pdf 


#24
Feb2112, 07:23 PM

P: 381

Going back to QED and the coupling constant. When higherorder terms in the perturbation series is used, the length scale becomes smaller. I wonder if this is the reason why the coupling constant becomes larger when more terms are used. Bill Hobba kept saying this but he didn't explain the physical reason why. Maybe it's because as more virtual particles or more terms are used, the length scale get smaller and smaller and hence the coupling constant secretly being dependent on how many terms means the coupling constant is equal to the sum of the feynmann vertex in the virtual particles interactions in 1st, 2nd, 3rd terms (I'm aware virtual particles are just the terms in the perturbation expansion so I'll use them interchangeably)? How do you understand this physically. 


#25
Feb2112, 07:58 PM

P: 381

Thanks for the updated descriptions. You'd make a great PF science advisor someday. Say, in the magnetic moment of the electron with measured value of 1.00115965219 and calculated value of 1.0011596522 in the fourth term in the power series. Did they use Renormalization Group there? Maybe the reason the second term to fourth term didn't produce an infinite coupling constant is because the calculation replaces it with 1/137 as you described. What then is the original coupling constant when no Renormalization Group procedure was used? 


#26
Feb2112, 08:22 PM

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PF Gold
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Thanks Bill 


#27
Feb2112, 08:53 PM

P: 381

note the interesting comments by Science Advisor tom.stoer that the Renormalization Group is just a DIRTY TRICK.
http://www.physicsforums.com/showthread.php?t=514073 Renormalization in perturbative QFT is constantly teached to be "removing divergences". Unfortunately this is only a dirty trick! Renormalization (nonperturbative renormalization) is something totally different  and it may even appear in systems w/o any divergences. Have a look at http://en.wikipedia.org/wiki/Renormalization_group 


#28
Feb2112, 09:07 PM

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PF Gold
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As one other person posted the fact it blows up to infinity means the theory is sick and incorrect  but we already know that because it gets replaced by the electroweak theory which will probably also get replaced by something else someday and that something else will hopefully be free of these problems. Thanks Bill 


#29
Feb2112, 09:14 PM

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PF Gold
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http://en.wikipedia.org/wiki/Effective_field_theory The only issue is theories like QED etc have a domain of applicability beyond which is does things like blow up to infinity  stick to that domain and everything is fine. Its hardly flabbergasting news and a DIRTY TRICK theories may not be valid to all energies. Thanks Bill 


#30
Feb2112, 09:35 PM

P: 381

My last question is this (I saw a similar question asked in the archives but unanswered). In the Dirac Equation. The magnetic moment of the electron is calculated as 1. In the 4th term in the power series, it's equal to 1.0011596522. The interacting fields are the electron self magnetic field and the electron. What about the interactions of say two electrons, what would be the Dirac Equation counterpart of 1.0 in the magnetic moment of the electron calculation? Do you calculate the dirac equation of each electron by adding them or calculate both of them combined? And if the result is for example 3.0. After the fourth term in the power series, would the result only be 3.0111 or would it be 5.0 (I don't think it would just be a small 3.0111 isn't it because the electric field strength is bigger). Thanks. 


#31
Feb2112, 09:46 PM

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PF Gold
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Thanks Bill 


#32
Feb2112, 10:33 PM

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#33
Feb2212, 04:34 AM

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#34
Feb2212, 04:36 AM

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http://www.mat.univie.ac.at/~neum/ms/ren.pdf to get a reasonably elementary explanation of renormalization and the renormalization group without any dirty tricks  is a simpler situation where everything can be understood explicitly. 


#35
Feb2212, 05:55 AM

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#36
Feb2212, 05:19 PM

P: 381

Before landau pole which is inside the planck length is reached.. one has to cross the planck boundary and much prior before that.. one has to touch first the electroweak length scale.. I'm not describing about using 100 Gev probe to unite the EM and Weak force.. but in Renormalization Group which is sensitive to the landau pole, it is sensitive to the electroweak pole too.. in this context, what is the length scale of the electroweak pole? Hope my questions are clear. If not. Just intuit what I'm saying and explain the details. Thanks.



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