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Effective field theory and Wilson's renormalization group 
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#1
Mar1512, 06:45 AM

P: 188

I have just read my first course on Quantum Field Theory (QFT) and have followed the book by Srednicki. I have peeked a bit in the books by Peskin & Schroeder and Ryder also but mostly Srednicki as this was the main course book. Now, I have to do a project in a topic not covered in the course and I have chosen Effective field theory (EFT), following the approach by Wilson. I have read the chapter(s) in Srednicki related to this topic a few times and understand (I think) the gist of the Renormalization Group (RG) and what it is about, but I can't say I understand the chapter on EFT (chapter 29 in Srednicki). I don't really understand what the EFT approach means and I was hoping that some of you could help me clear this up.
As I understand it, when we use the MSbar renormalization scheme, the parameters in the lagrangian no longer represent the physical parameters (for example, the m term is not the physical mass) and we can find equations that tell us how the lagrangian parameters vary with the fake parameter μ (any final answer can't depend on μ). This can also be done with the RG approach in a more formal way (as I understand it, the result is the same  we get a group of equations that tell us how the lagrangian parameters vary). However, the next chapter on EFT:s I struggle to understand. I get that we have a cutoff [itex]\Lambda[/itex] for the momentum and that we can try to see what the theory tells us at momenta well below the cutoff but then a new cutoff [itex]\Lambda_0[/itex] is introduced and I must say I don't understand the difference between the two. Something I would also like to get some help with is how Wilson's approach with EFT:s relates to renormalization. Why does the EFT approach remove the necessity for a theory to be renormalizable? Any help and clarifications is highly appreciated! 


#2
Mar1612, 11:07 AM

Sci Advisor
P: 779

Check out this review
http://arxiv.org/pdf/nuclth/9506035.pdf and the many references therein. This was where I first started to learn about this stuff. Actually, my colleague and I are working on a textbook on "Effective Field Theory", but it won't be done for a while. Stay tuned..... 


#3
Mar1612, 11:57 AM

P: 308

you should also read Wilson's original papers on the topic. They're pretty clear and really show why renormalization is a completely sensible and physical thing to do. Unlike the "sweeping infinities under the rug" perspective which many people don't like (for some reason I never understood)



#4
Mar1612, 09:18 PM

P: 216

Effective field theory and Wilson's renormalization group
As far as I can understand, Srednicki uses BPH/counterterm renormalization. So the bare parameters in the theory are actually physical parameters: you perturb about the physical system but this comes at the expense of requiring counterterms. 


#5
Apr1012, 02:30 PM

P: 23

Hi
see the following lecture by Rothstein TASI Lectures on Effective Field Theories this lecture can be downloaded via the link arxiv.org/pdf/hepph/0308266 


#6
Apr1012, 03:13 PM

P: 23

Hello,
if you interested on Effective Field theory then look at titles below References on Effective Field theory 1 Georgi, Effective Field theory www.people.fas.harvard.edu/~hgeorgi/review.pdf 2A. Pich, http://arxiv.org/pdf/hepph/9806303 3video lectures by Cliff Burgess * at the website http://pirsa.org/C09020 4 arxiv.org/pdf/hepth/0701053 by Burgess 5 Five lectures on effective field theory http://arxiv.org/abs/nuclth/0510023 by Kaplan 6http://arxiv.org/abs/nuclth/9506035 also by Kaplan 


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