Was trying to understand renormalizability in EFT. This is a little confusing especially the part of the misnomer. Can someone please explain this?

Text taken from Wikipedia:

"However, in an effective field theory, "renormalizability" is, strictly speaking, a misnomer. In a nonrenormalizable effective field theory, terms in the Lagrangian do multiply to infinity, but have coefficients suppressed by ever-more-extreme inverse powers of the energy cutoff. If the cutoff is a real, physical quantity—if, that is, the theory is only an effective description of physics up to some maximum energy or minimum distance scale—then these extra terms could represent real physical interactions. Assuming that the dimensionless constants in the theory do not get too large, one can group calculations by inverse powers of the cutoff, and extract approximate predictions to finite order in the cutoff that still have a finite number of free parameters. It can even be useful to renormalize these "nonrenormalizable" interactions."

  • $\begingroup$ What is "EFT"? Effective field theory? Also, what is confusing your about the text you quote? $\endgroup$ – ACuriousMind May 17 '15 at 21:29
  • $\begingroup$ The whole text is confusing, how come renormalizability is a misnomer in effective field theory via this argument? How and why do coefficients suppressed by extreme powers of energy cutoff kick in? Why get suppressed? What do they imply? $\endgroup$ – Beyond-formulas May 17 '15 at 21:37
  • $\begingroup$ This is just an example of the very poor quality of the physics material on wikipedia. Read ``Is renormalizability necessary'' in Vol I of Weinberg (or any other decent text book on modern QFT or EFT methods). $\endgroup$ – Thomas May 18 '15 at 0:08

The article assumes that the reader thinks that the point of renormalization is removing infinities. What it is saying is that that issue of renormalization is not simply about removing infinities but about how physics changes as scales change. This concept is much more general and can be applied to situations when there are no infinities in sight like in condensed matter systems.


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