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Renormalization Group for dummies 
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#37
Feb2212, 06:20 PM

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#38
Feb2212, 06:24 PM

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PF Gold
P: 2,896

Regarding the Landau pole although it is an issue it is calculated perturbatively and the region in blows up is one where perturbation theory will not work because it is so large. However renormalisation group theory does and it shows it blows up in a different way  but blow up it does. Thanks Bill 


#39
Feb2212, 06:39 PM

P: 381

Do you agree that we only do renormalization group calculations because the theory we have is only an effective field theory. Meaning when we come to the final true theory, we don't have to use any renormalization group, can anyone refute this? 


#40
Feb2212, 07:14 PM

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PF Gold
P: 2,896

Thanks Bill 


#41
Feb2212, 07:21 PM

P: 381

"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." But QED is because of the broken symmetry where electromagnetism and the weak force is not united because of the low energy. Are you saying that near the planck length, the electroweak force is active and this QED probe can still touch it? I know we need 100 Gev probe to touch it.. but in ordinary em field, can it probe the electroweak scale? 


#42
Feb2312, 10:58 PM

P: 381

There's this very interesting book called: "The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe"
http://www.amazon.com/InfinityPuzzl...0058226&sr=81 It's a laymen book and Renormalization Group was not mentioned however it seems to be related to the older Mass and Charge Renormalization used by Feynman, Schwinger, Tomonaga mentioned up to Chapter 3 which I just finished. Going to wiki. "In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales." My questions are how come the Renormalization Group was attributed to Kenneth Wilson when in fact even Feynman, Schwinger, Tomonaga used it called Mass and Charge Renormalization. And what would happen if you use the Kenneth Wilson's "Renormalization Group" on QED. Noting Wiki: "They effectively devised the theory of mass and charge renormalization, in which the infinity in the momentum scale is cutoff by an ultralarge regulator, Λ" Anyone has other perspective of this or can in a very sentences give some quick insight? What I'm saying is that the infinityinfinity thing is related to mass and charge renormalization as mentioned by "The Story of Light" But wiki seems to be saying that this also used the regulator thing used in Wilson full Renormalization Group. Thanks. 


#43
Feb2312, 11:47 PM

P: 381

http://www.physicsforums.com/showthread.php?t=183903 msg #2 by Eugene: "In the end of 1920's Dirac, Pauli, Weiskopff, and Jordan formulated a quantum theory of interactions between electrons and photons in a loose analogy with Maxwell's classical electrodynamics. This early quantum electrodynamics (QED) was very successful in calculations of various scattering processes in lowest orders of the perturbation theory. Unfortunately, all contributions to the Smatrix in higher orders came out infinite. In late 1940's Tomonaga, Schwinger and Feynman found the way to fix this problem of infinities by renormalization. The renormalization basically adds certain infinite counterterms to the Hamiltonian of the early QED. The form of these counterterms was selected such that the resulting theory satisfied two physical principles. First, the calculated electron's mass should be equal to the measured electron's mass. Second, the calculated interaction energy between two electrons at large distances should be equal to the classical expression e2/r. These two requirements lead to two types of renormalization counterterms in the Hamiltonian  the mass and charge renormalization counterterms." And http://www.physicsforums.com/showthread.php?p=3628984 in msg #20 by atyy: "Probably the chief conceptual advance since Feynman's original work (not the book, which is late), is why renormalization works. This is provided by "renormalization group" and "effective field theory ideas". The basic idea is that we don't need theories that are consistent at all energies. They just need to work at low energies. Renormalization flow is the process of seeing what a theory given only its symmetries "looks like" at lower and lower energies. A "renormalizable theory" like QED is one in which the flow converges to a fixed point, about which perturbation theory can be done." My questions. What happens if you apply the modern Renormalization Group" idea to the Feynman era QED problem? How would it differ then to the mass and charge renormalization techniques? 


#44
Feb2412, 01:34 AM

Sci Advisor
PF Gold
P: 2,896

You seem to stuck on the renormalization group  its not required to do renormalization  simply to better understand whats going on. It does not change the method one whit which is a way of adding counterterms to ensure what you get is finite. But the math of that is quite complicated  good luck in finding someone to explain it  you really need a textbook. Thanks Bill 


#45
Feb2412, 02:15 AM

P: 381

"I may be wrong but it sounds as if you imply that an effective field theory approach implies the assumption of granularity of spacetime (I may have misinterpreted your words, if so I apologize). Saying that a theory is an eft does not imply that. It just implies that at some scale "new physics" arises. The nature of this new physics is quite arbitrary, it could be granularity of spacetime but it could be a new force, inner structure to the particles (including stringlike structure) etc etc etc. So in that sense it is quite general." There is another possibility, related to the foundations of QM. If one take the view of Bohmian Mechanics, there may be no virtual particles taking all paths and the infinity problem resulting from all this amplitude pathintegral approach like stuff because in the world of Bohmian Mechanics, particles are always particles. Hope a Bohmian for example Demystifier can confirm whether this is true. Btw.. Feynman being a genius that he was. How come he didn't arrive at the Renormalization Group idea himself (about coupling constant depending on the cutoff) while mulling about it. Could there be a development in physics later on that popularize the idea which Feynman didn't dare think about? Anyone got a clue? 


#46
Feb2412, 02:17 AM

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P: 8,781

The final results, at an energy scale E well below the initial cutoff λ0, are the same as we would predict via renormalized perturbation theory, up to small corrections by powers of E/λ0. " The advantage of the Wilson scheme is that it gives a nonperturbative definition of the theory which is applicable even if the theory is not weakly coupled. ..." "The Wilson scheme also allows us to give physical meaning to nonrenormalizable theories. Given an action for a nonrenormalizable theory, we can regard it as an effective action. ..." 


#47
Feb2412, 02:48 AM

Sci Advisor
PF Gold
P: 2,896

Thanks Bill 


#48
Feb2412, 07:55 PM

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http://www.physicsforums.com/showthread.php?t=75307 http://www.physicsforums.com/showthread.php?t=460685 


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