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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Wilsonian EFTs and regularization

**Physics Forums | Science Articles, Homework Help, Discussion**