Effective Field Theories
Round 1
Reviewer 1 Report
The work presents a "pedagogical introduction to low-energy effective field theories", where effective Lagrange Functions are built to describe QED and QCD.
While the general idea for this work is interesting, one should note that the presentation is far form being "pedagogical". Many important references are missing for a student interested in learning more about the field, and the manuscript is biased too strongly in the direction of effective theories, without mentioning the fundamental concepts involved in scale invariance, so important in Yang-Mills Theories. In fact, the author claim, at the Conclusion that "At present we accept the fact that our theories only describe the Nature at sufficiently low
energies (or sufficiently large distances). They are effective low-energy theories.", hidden the fact that scale invariance is fundamental to allow renormalization at any scale, what is a much more fundamental characteristic than the possibility to use perturbative methods.
Thus, despite the interest in a pedagogical approach to effective theories, the present work fails in both senses: it is not truly pedagogical, and it is biased in a direction that can be misleading to students that are entering the field.
A careful revision of English Grammar would make easier for students to understand what the author means. In particular, some sentences are made in order the reader have to "guess" which message is conveyed by the author, what is not really pedagogical.
In my opinion the work can be improved by including in the introduction a thorough description of the scale invariance, and then show how effective theories can be used to access the physics far from the scale that breaks the scale invariance. Avoiding statements that can be erroneous or misleading would be a good practie if one is addressing the paper to students. Therefore I would ask the author for a major modification of his work along these lines.
Author Response
I'm sorry but I really cannot understand what the reviewer says. "the manuscript is biased too strongly in the direction of effective theories" Yes, it is only about effective theories. This follows from its title. It is not supposed to discuss other aspects of quantum field theory. "without mentioning the fundamental concepts involved in scale invariance" Why should scale invariance be discussed here? The Nature is not scale invariant. Electrons and protons have some definite masses, thus clearly demonstrating this fact. When we discuss the relationship between some theory and a low-energy approximation to it, there is always some very specific scale, typically the mass of some heavy particle, where the effective theory breaks down. So, the very possibility to introduce a low-energy effective approximation is based on the fact that the more fundamental theory is not scale invariant. It contains some intrinsic scale; at energy scales much lower than it we may use a simpler effective theory instead of the more complicated full theory. "scale invariance is fundamental to allow renormalization at any scale" Why? QED is not scale invariant: it contains the electron mass. But it is renormalizable. The first example considered in my lectures is exactly based on this non-scale-invariantness of QED. If we consider energy scales much lower than m_e, we can approximate QED by a simpler effective theory of photons. It the full theory were scale invariant, it would be impossible to say that at low energy scales it can be approximated by an effective theory. Low scales compared to what? So, I must confess that I have understood nothing from this review, and have no idea what changes of the text of my lectures should be done, from the reviewer's point of view.Reviewer 2 Report
The review is very well written and clear. It also has a great pedagogical value, thereby I recommend it for publication, the followings are the details:
The scientific soundness (which is what counts most for me in a scientific paper) is not in question and I will not discuss it here.
About the pedagogical issue. In fact the reader has to have already a certain background of Quantum Field Theory (QFT) in order to understand what the author says. I also partly disagree with him because in only 26 pages one cannot really expect to be so exhaustive, without being naive or trivial, about a topic as large as QFT, even if considered from the special point of view of Effective QFT. Therefore I already expected a certain degree of sophistication. There are in fact many entire QFT books which are merely introductions to the subject, so I guess a simple 26 pages review needs to be somehow “more difficult to follow”, so to say.
As for the English grammar, I am afraid that English is not my mother tongue, so I might not be entitled to formulate a judgment about the author’s proficiency in this language. I could read the text with no problems, so I assumed that the English level was just fine.
Author Response
"the reader has to have already a certain background of Quantum Field Theory (QFT) in order to understand what the author says" Yes, the students are supposed to know basic things about QFT, including renormalization. "in only 26 pages one cannot really expect to be so exhaustive, without being naive or trivial, about a topic as large as QFT, even if considered from the special point of view of Effective QFT" I completely agree. This paper is my lectures at two summer schools. In each case I had 3 hours. It is not possible to say much during 3 hours. "There are in fact many entire QFT books which are merely introductions to the subject" Of course. I know only one book entirely about effective field theories: A.A.Petrov, A.E.Blechman, Effective field theories, World scientific (2016), 320 p. But I could not present all the material in these 320 pages during 3 hours. I had to choose only some simplest examples. "a simple 26 pages review needs to be somehow “more difficult to follow”" I'm afraid I don't understand what you say here. Do you mean that I should make the text more difficult to follow?