Infrared Regularization of Very Special Relativity Models
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear author:
I greatly enjoyed your work, "Infrared Regularization of Very Special Relativity Models". Nevertheless, some commentaries, in form but not in substance, must be improved to be suitable for publication. After that, I will decide:
1. Firstly, all acronyms are generally reserved for the introduction, not for the abstract (VRS and QED). The abstract is the first appreciation of your ideas and results. Please change these in the introduction.
On page 1:
2.- I think author must join lines 15-22 in only one paragraph. The same task is for lines 35-43.
On page 2:
3.- As before, I think the author must join lines 66-73 in only one paragraph.
4.- I think that author must join lines 83-84 in only one paragraph.
5.-In line 81, I suggest changing "In Section 8 we draw some conclusions" to "Section 8 is devoted to the conclusions and discussions."
6. To add a dot to the equation after line 84 and a comma after line 85.
On page 3:
7.-To add a dot to the equation after line 95, 97 and 98 (I suggest here to consider q_{\mu} \mbox{arbitrary.}), a comma after line 96.
8.-I think that author must join lines 99-102 in only one paragraph.
9.-On eqs. after lines 103,104,107 and 114, please add a dot. For the eq. after line 113, please add a comma.
On page 4:
10.- There is a typo in line 120, please fix it.
11.-In line 131, I suggest changing "$\bar{n}_{\mu}->0$" to "$\bar{n}_{\mu} \rightarrow 0$.
12.-Please improve lines 137-138 and 142-143.
13.-On eq. (2) please add a comma. On eqs. (3) and (4) please add a dot.
14.-I think that the author must join lines 154-155 in only one paragraph.
On page 5:
15.-Please improve eqs. (5)-(6).
16.-As before, in lines 157 and 159, I suggest changing "$\bar{n}_{\mu}->0$" to "$\bar{n}_{\mu} \rightarrow 0$.
17.-On eqs. (7)-(8) and after line 169, please add a dot.
18.-I think author must join lines 164-166 in only one paragraph.
On page 6:
19.-On eqs. (9), (12), (13) and (14), please add a dot. On eq. (10), add a comma.
20.-On Figures 2-3 add a comment with respect to the contribution to the two dimensional axial vector current in VSR Electrodynamics.
On page 7:
21.-In lines 191 and 198, I suggest changing "$\bar{n}_{\mu}->0$" to "$\bar{n}_{\mu} \rightarrow 0$.
22.-I think that the author must join lines 192-193 in only one paragraph.
23.- On eqs. (17), (18), (19), (20) and (23), please add a dot.
24.-There is a double numeration on eqs. (21)-(22).
On page 8:
25.-On eqs. (24) and (25), please add a comma. On eqs. (26), (27) add a dot.
26.-IMPORTANT: After line 225 there is a problem with the letter size, please fix it and add commas and dots where required here.
On page 9:
27.-On Figures 4-6 add a comment with respect to the diagrams.
On page 10:
28.-On Figure 7 add a comment with respect to the diagrams.
On page 11:
29.-On Figure 8 add a comment with respect to the diagrams.
30.-I think that the author must join lines 271-272 in only one paragraph.
On page 12:
-In your conclusions, which open problems can arise from this work?.
Comments on the Quality of English LanguageIn my opinion, there are some typos in the document, but there are no issues with respect to the quality of the English language broadly.
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper studies the axial vector current, which includes γ5 Dirac matrix, in Very Special Relativity (VSR) models. In VSR models, kinetic terms are modified by a mass m and a null vector n. Then, the author computed Feynman diagrams by using modified propagators and analyzed the axial vector currents in certain models. The author found the violation of current conservation at the quantum level by nonzero m. Also, a new phase in the large N Gross-Neveu model by nonzero m was found.
I'm not sure that VSR models are useful in real experimental physics. But, the formalism with modified propagators by nonzero VSR mass m is interesting and seems to be correct. And I also think that a new phase in the large N Gross-Neveu model is an interesting phenomenon. So, the content of this manuscript is good.
However, the writing style of the paper is terrible. I think line breaks and spaces between sentences in this draft are not appropriate. In particular, there are too many line breaks at the beginning of Introduction.
After minor revision of the writing style, I recommend this paper for publication in Universe.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis paper presents some interesting calculations, and I think eventual publication would be appropriate. The manuscript is, however, in need of definite editing.
Besides mechanical, formatting, and referencing oversights, there is also a lot of confusing terminology. Strictly, speaking, VSR refers to theories with a class of multiple possible symmetries. SIM(2) is, in fact, the largest VSR symmetry group that it is possible for a theory to have while still falling short of full Lorentz symmetry. It is also possible to have VSR groups with smaller T(2), E(2), or HOM(2) subgroups of SIM(2). This terminological issue ought to be clarified.
The terminology used for VSR-like theories in 1+1 dimensions (the Schwinger model, etc.) is also inaccurate. In the manuscript, these models are often described as having the SIM(2) symmetry, but in fact the true symmetry group is actually much smaller—as ought to be expected in a theory with only a single spatial dimension.
Sections 4 through 6 seem to retread the same essential material multiple times. It would be better to condense and reorganize the calculations, rather than completing them repeatedly with relatively minor variations. This seems especially the case because the author has previously calculated the chiral anomaly in a massive theory, which ought to be more general than a massless one
Near the beginning of section 7, it says that four graphs are needed for the axial vector anomaly in 3+1 dimensions. However, it lists the wrong figures, and even looking at the three correct figures, there are quite obviously five or six graphs, not four.
However, with these kinds of changes made, I would recommend eventual publication.
Comments on the Quality of English LanguageTo start with, there are mechanical problems with the paper. The paragraphs break in peculiar places, sentences end prematurely, notation is not always consistent or explained, and references are apparently out of order.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
