Hi folks - I have a couple of questions about EFTs that are driving me crazy.(adsbygoogle = window.adsbygoogle || []).push({});

(1 ) Consider first of all a Wilsonian effective Lagrangian - one in which particles of mass >M have been integrated out from a 'full' Lagrangian leaving a string of non-renormalizable interactions amongst the light particles. If we want to make predictions using this theory, we will need to use a renormalization scheme. In so doing, are we

(a) compelled to use a momentum-space regularization, with the cut-off placed at M;

(b) are we forbidden to take this cut-off to infinity, thus committed to viewing spacetime as a lattice?

(I am wondering this because I'm wondering if you can use the Wilson technique for making effective Lagrangians and still have the resulting EFT defined on a continuum. I'm also wondering this because the two kinds of cut off used in the Wilsonian picture - at least as presented in Peskin and Schroeder - seem conceptually distinct: one is telling us which physical particles are going to be relevant at a given energy, the other cutting off the types of virtual particles that might contribute. But maybe these two roles are after all one and the same role.)

(2) Now for a question on dimensional regularization. With a momentum cut-off we can at least make sense of not taking the cut-off to infinity (putting the violence that it does to Poincare invariance and the structure of spacetime). Is there any sense in using dimensional regularization and not going to the d=4 limit at the end of the calculation? That is, do we have the option of not removing the 'cut-off' in this case?

Any thoughts or references would be most appreciated!

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# Wilsonian EFTs and regularization

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