Why Poincare Symmetry Is a Good Approximate Symmetry in Particle Theory

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please, see the referee report.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Quality of English text: OK!

Author Response

I am very grateful to Reviewer 1 for his/her positive assessment of my paper and important comments.

The first comment was: “Before eq. (15), the text in semiclassical approximation, the operators M_ab can be replaced by their numerical values looks strange, so maybe the author can reformulate it.” In the revised of the paper, I explain the meaning of semiclassical approximation. I hope that, given this explanation, it will be clear to readers why, in this approximation, operators can be replaced by their mean values.

Considering the second and third comments of Reviewer 1, the paper was slightly revised.

I am grateful to Reviewer 1 for pointing out literature on the topic of the paper. In the revised version of the paper, the Reviewer's references are included in the list of references.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Report on the paper
Symmetry in particle theory
by Felix M Lev
Considering the Poincare symmetry is a good approximate symmetry in certains conditions, the author's aim is to show that explicit solutions with certain properties exist within the framework of the approach proposed by Flato and Fronsdal.
It is shown that there exist scenarios when Poincare symmetry works with a high accuracy.
The paper is well written and it gives the reader a good image of the studied problem.
I recommend the publication.

Author Response

I am very grateful to Reviewer 2 for his/her positive assessment of my paper.

Reviewer 3 Report

Comments and Suggestions for Authors

In this very interesting paper, the Author tries to answer the question why in particle physics, Poincaré symmetry
works with very high accuracy. The usual answer to this question is that a theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space becomes very large. However, de Sitter and Minkowski spaces are purely classical concepts, while in quantum theory (and in particular in particle theory) the answer to this question has to be given only in terms of quantum concepts. As noticed, Poincaré symmetry is a good approximate symmetry if the eigenvalues of the operators are much larger than the eigenvalues of the operators. In this paper it is shown that explicit mathematical solutions exist under suitable and reasonable properties. This is certainly interesting because there are many examples where some theoretical questions have been solved in a purely mathematical way
but the physical meaning of the solution has been understood
only after some time (the most famous of these examples is the Dirac positron). So having found mathematical solutions is very important.
Moreover, this paper is written in an elegant way and in fluent English. For these reasons, I strongly recommend the publication on Simmetry.

Author Response

I am very grateful to Reviewer 3 for his/her positive assessment of my paper.