General Quantum Field Theory of Flavor Mixing and Oscillations
Round 1
Reviewer 1 Report
The paper tries to address the problem of quantum field mixing via Bogoliubov transformation. A general mixing relation is proposed, the flavor vacuum is constructed explicitly and time dynamics
are discussed. Possible applications in vector meson mixing and fermion mixing are provided. The paper is well-written and the subject is of theoretical importance. However, it should not be considered for publication as nearly all the major results in this paper are identical to that of a published paper by the same authors, Phys.Rev.D 65 (2002) 096015. From now on it will be referred to as “the PRD paper” for convenience.
Following the ordering of the paper, Section 2 gives a general introduction of canonical transformation first, then introduces Bogoliubov transformation and shows its applications in superfluidity
and low-energy QCD. None of these are original. Section 3 contains the main results of the paper as the author addressed in both abstract and the conclusion, but it is the same as Section 2 and Section 3 of the PRD paper. The only new things appear in Section 4, from Eq.(3.6) to Eq.(3.14), but I failed in seeing the importance of them. The supplemental materials shown in the Appendices are identical to those of the PRD paper.
To view this paper as a review, I find it relies too heavily on the authors’ own work and the development of the whole field is not suitably addressed. For the above reasons, I cannot recommend it for publication.
There are some minor suggestions:
The labeling of the equations in Section 3 and 4 should be changed like Eq.(n.xx) to Eq.(n+1.xx).
On Page 5, the authors may want to change the two “superconductivity” into “superfluidity”.
Figure 2.1 helps little in understanding, if not contributes to confusing.
The references are not up-to-date, and the latest one is published in year 2005. If there were no development at all in the field, the authors may need to explain why and emphasize what real progress this paper makes.
Author Response
"Please see the attachment"
Author Response File: 
Author Response.docx
Reviewer 2 Report
The authors report about one of the most interesting problems in today's particle physics. The paper is well written and scientifically sound. In my opinion, it deserves to be accepted for publication.
Author Response
"Please see the attachment."
Author Response File: Author Response.docx
Reviewer 3 Report
The authors give a general overview of the use of canonical transformations in quantum mechanics, quantum many-body physics and quantum field theory, focusing on the important case of Bogoliubov transformations. Then the relevant case of general quantum field mixing is considered in detail.
The paper is well written and organized. The inclusion of Section 2 makes the paper interesting to a wide audience. Also appropriate is the choice of the material to be relegated in the appendices.
I only have a minor comment. Below line 155 (p.5) the authors refer to Bogoliubov's 1947 paper (ref. [39]), asserting that in it Bogoliubov introduced the transformations that now bear his name in order to build a microscopic theory of superconductivity. However (as correctly stated by the authors on p. 6), Bogoliubov's aim in that paper was rather to develop a theoretical explanation of superfluidity; the method was extended to superconductivity by Bogoliubov himself and Valatin in 1958, after the BCS theory appeared (Bogoliubov, N.N. On a new method in the theory of superconductivity. Nuovo Cim 7, 794–805 (1958); Valatin, J.G. Comments on the theory of superconductivity. Nuovo Cim 7, 843–857 (1958) ).
I also would like to make the following minimal linguistic suggestions:
-Line below line 280, p. 16: I would write "pursue a slightly different strategy".
-Line 362, p. 19: I would write "an EPR-coherent".
Author Response
"Please see the attachment."
Author Response File: Author Response.docx
Reviewer 4 Report
I think the authors present a good comprehensive review on the approach to the flavor mixing based on Bogoliubov transformation. The way of the presentation is very general and we expect that the method can be applicable to different fields. The authors also devote one section to the mass parameter issues of this approach. I think the paper is useful for the further understanding of the flavor mixing phenomena. Considering above, I think the paper is worth for publication of the Journal "Universe".
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There are the following typos.
(1) In Eq.(2.10), the helicity " sigma' "should be sigma.
(2) In the definition of Lambda(\theta, t) below Eq.(3.1), in the exponential,
"theta" is missing.
Author Response
"Please see the attachment."
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
I accept the authors' explanations.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
