Effective field theory and Wilson's renormalization group

[kloptok]

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As I understand it, when we use the MS-bar renormalization scheme, the parameters in the lagrangian no longer represent the physical parameters (for example, the m term is not the physical mass) and we can find equations that tell us how the lagrangian parameters vary with the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 cut-off $\Lambda$ for the momentum and that we can try to see what the theory tells us at momenta well below the cut-off but then a new cut-off $\Lambda_0$ 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!

 

[blechman]

Check out this review

http://arxiv.org/pdf/nucl-th/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...

 

[negru]

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)

 

[geoduck]

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 MS-bar 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 cut-off $\Lambda$ for the momentum and that we can try to see what the theory tells us at momenta well below the cut-off but then a new cut-off $\Lambda_0$ 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!

I think the difference between Wilson's approach is that you are not taking the cutoff to infinity, and hence your results will be finite, whereas in standard renormalization you are taking the cutoff to infinity. You can begin from a renormalizable theory (i.e. one in which cutoff can go to infinity) and integrate out ultraviolet modes, allowing you to henceforth integrate to a finite cutoff, but this comes at the expense of having to calculate an infinite number of new interactions which would ordinarily be unrenormalizeable. Luckily however, you don't need to know the values of the coefficients for the new interactions that are unrenormalizeable, because by integrating out more momenta, the coefficients take on values gotten by the renormalizeable terms at the momenta you just integrated out. What has me confused is that when your cutoff becomes extremely low from integrating momenta out, then these unrenormalizeable terms become very important, as they go as 1/cutoff. So at very low energies shouldn't the unrenormalizeable terms dominate over the renormalizable ones?

As far as I can understand, Srednicki uses BPH/counter-term 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 counter-terms.

 

[mwalmasri]

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

 

[mwalmasri]

references on Effective field theory

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
2-A. Pich, http://arxiv.org/pdf/hep-ph/9806303
3-video lectures by Cliff Burgess * at the website http://pirsa.org/C09020
4- arxiv.org/pdf/hep-th/0701053 by Burgess
5- Five lectures on effective field theory http://arxiv.org/abs/nucl-th/0510023 by Kaplan
6-http://arxiv.org/abs/nucl-th/9506035 also by Kaplan