Asymptotic States and S-Matrix Operator in de Sitter Ambient Space Formalism
Round 1
Reviewer 1 Report
----------------------------------------------------------------------
Report on manuscript ID: Universe–2504865
----------------------------------------------------------------------
This work represents an application to investigate the possibility of the existence of the S-matrix operator for de Sitter QFT (de Sitter ambient space framework). Such an investigation is based on the previous existence of asymptotic states in de Sitter QFT The authors also proposed some discussion exploring the differences and similarities between QFT in Minkowski and de Sitter spaces.
The paper is well presented overall, the set of references chosen is well-situated and the mathematical manipulations in this paper may be correct (I have not checked all of them). Although the topic is of interest for particular readers, I believe this paper fulfills the standards requested by this journal, with some explanation in the present version (please, see my questions below), I recommend it for publication in Universe.
1) a) On page 3, subsection 2.1 the authors decided to use $c=1$. Due to this, I could not understand why in Eqs. (2.1), (2.2) and (2.3) they are still using $c$. I think the authors should rewrite these equations and throughout the text.
b) Also in Eqs. (2.1), (2.2) and (2.3) and throughout the text, $\hbar$ maybe can set as 1.
2) On page 3, I think this is the first time that we can see $\nu$. Is it only a mathematical parameter or is the any physical meaning?
3) On page 4, I think there is some mistake “… delta distribution (see Eqs. (2.30) – (2.30) for more details)…”, I mean Eqs (2.30) – (2.??).
4) On page 4, subsection 2.2, the authors claim “we note that the scalar case can be generalized to the various massive or massless fields with nonzero spin,….” I think the author should provide some reference(s) dealing with such cases (higher spin).
5) On page 11, the author used “the adiabatic hypothesis conditions in the interaction case within the framework of dS ambient space formalism…”, just likewise in the Minkowski spacetime [24]. Is the any reference doing the same approach as the authors have done? Is there any guarantee that procedure will work in the dS ambient space formalism?
6) On page 13, section 4, the authors claim “Note that this effect that we have explained here can be generalized to other spin fields.” Please see my comment #4.
7) Finally, the abstract says, “The authors also proposed some discussion exploring the differences and similarities between QFT in Minkowski and de Sitter spaces.” Maybe I’m mistaken but I could not see such discussions. I think the author should insert those discussions explicitly in the conclusions section.
%%%%%%%%%%%%%This ends my report%%%%%%%%%%%%%%%%
Comments for author File: 
Comments.pdf
Author Response
Dear Reviewer
We are pleased to submit a revised version of our manuscript with ID: universe-2504865, entitled Asymptotic states and S-matrix operator in de Sitter ambient space formalism.
In preparing this new version we have attempted to follow as much as possible your recommenda- tions/suggestions regarding our paper. We have revised our manuscript as follows and added material is red marked in the complementary pdf.
Your points and our answers:
-
a) On page 3, subsection 2.1 the authors decided to use c = 1. Due to this, I could not understand why in Eqs. (2.1), (2.2) and (2.3) they are still using c. I think the authors should rewrite these equations and throughout the text. b) Also in Eqs. (2.1), (2.2) and (2.3) and throughout the text, ~ maybe can set as 1.
Our reply to a) & b): At the top of Page 3, we motivate the temporary use of the constants c and ~. After the fourth paragraph of Subsection 2.1, we return to the atomic units c = 1 = ~, as is made precise in the text (with red color).
-
On page 3, I think this is the first time that we can see ν. Is it only a mathematical parameter or is the any physical meaning?
Our reply: Notation ν is the dS invariant parameter that classifies the UIR of the dS group and it is properly defined and discussed on pages 2 and 3 (see red-marked sentences). In specific cases, its physical meaning is related to a mass as shown in Eq. (2.1).
-
On page 4, I think there is some mistake “... delta distribution (see Eqs. (2.30) – (2.30) for more details)...”, I mean Eqs (2.30) – (2.??).
Our reply: The equation numbers are corrected (with red color) in Page 4.
-
On page 4, subsection 2.2, the authors claim “we note that the scalar case can be generalized to the various massive or massless fields with nonzero spin,....” I think the author should provide some reference(s) dealing with such cases (higher spin).
Our reply: Generalisations to non-zero spins are possible, and references have been added in Page 4, Line 150.
-
On page 11, the author used “the adiabatic hypothesis conditions in the interaction case within the framework of dS ambient space formalism...”, just likewise in the Minkowski spacetime [24]. Is the any reference doing the same approach as the authors have done? Is there any guarantee that procedure will work in the dS ambient space formalism?
Our reply: Concerning the first question, in the new version we have inserted more explanations and references about our motivations in introducing the adiabatic hypothesis for QFT in dS space-time. In this regard, new sentences and references have been added in Page 11 (with red color). For the Referee’s second question, besides its physical validation (which would require observational data within a dS environment), our adiabatic hypothesis is mathematically well- defined in the dS ambient space formalism.
-
On page 13, section 4, the authors claim “Note that this effect that we have explained here can be generalized to other spin fields.” Please see my comment #4.
Our reply: See our answer to point 4. Moreover, relevant references have been added in Page 13, at the end of the conclusion.
-
Finally, the abstract says, “The authors also proposed some discussion exploring the differences and similarities between QFT in Minkowski and de Sitter spaces.” Maybe I’m mistaken but I could not see such discussions. I think the author should insert those discussions explicitly in the conclusions section.
Our reply: Concerning Referee’s suggestion in Point 7, we have considered this question in many places throughout the text, in the introduction, in Section 2, at various places in Section 3, particularly in Subsection 3.1. In the new version, we also added a sentence in the conclusion section (with red color).
We take this opportunity to thank you for precise comments which help us to improve the content of our article.
Sincerely yours
M.V. Takook, J.-P. Gazeau, E. Huguet
Reviewer 2 Report
In this paper, the authors studied the existence and completeness of asymptotic states for massive scalars in 4d de Sitter spacetime. Since 4d de Sitter spacetime can be embedded in 5d Minkowski spacetime, one can generalize useful theorems for Minkowski spacetime to theorems for de Sitter spacetime. By using these theorems, the authors showed the existence and completeness of asymptotic states, where the asymptotic states are defined in an observer-independent way.
In the S-matrix formalism, the existence and completeness of asymptotic states are crucial starting points, whose proof is very important. So, the proof for de Sitter spacetime in this paper is a good outcome for the community. The proof in subsection 3.2 is explained clearly, and it is easy to see where the authors use the results in subsection 3.1.
Before the publication, I have one question about (3.9). The adiabatic hypothesis means that interactions should vanish at future and past infinity. But, (3.9) shows the adiabatic hypothesis at past infinity only. Can we derive the adiabatic hypothesis at future infinity from (3.9)? Or do we need to assume the adiabatic hypothesis at also future infinity? I would like to see this point clearly written.
And I also have a comment about \equiv. The authors used \equiv for definition and equivalence. For example, \equiv in (2.33) and (2.39) is used as definition, and \equiv in (3.11) is used as equivalence between Hilbert spaces. I think that the authors should use different notations for definition and equivalence.
Once the above corrections are made, I recommend the paper for publication in Universe.
Author Response
Dear Reviewer
We are pleased to submit a revised version of our manuscript with ID: universe-2504865, entitled Asymptotic states and S-matrix operator in de Sitter ambient space formalism.
In preparing this new version we have attempted to follow as much as possible your recommendations/suggestions regarding our paper. We have revised our manuscript as follows and added material is red marked in the complementary pdf.
Your points and our answers:
-
Before the publication, I have one question about (3.9). The adiabatic hypothesis means that interactions should vanish at future and past infinity. But, (3.9) shows the adiabatic hypothesis at past infinity only. Can we derive the adiabatic hypothesis at future infinity from (3.9)? Or do we need to assume the adiabatic hypothesis at also future infinity? I would like to see this point clearly written.
Our reply: Concerning the second Referee’s first question a sentence has been added in Page 11, below Eq. (3.9) (with red color).
-
And I also have a comment about ≡. The authors used ≡ for definition and equivalence. For example, ≡ in (2.33) and (2.39) is used as definition, and ≡ in (3.11) is used as equivalence between Hilbert spaces. I think that the authors should use different notations for definition and equivalence.
Our reply: Concerning this point the Referee is right and we have replaced the symbol “≡” with just “=” when the former in unnecessary, and we have replaced “≡” with “≃” for isomorphism between Hilbert spaces.
We take this opportunity to thank you for precise comments which help us to improve the content of our article.
Sincerely yours
M.V. Takook, J.-P. Gazeau, E. Huguet
Round 2
Reviewer 2 Report
The authors properly responded to my requests. So, this paper is fine for publication in Universe.
