Quantum Vacuum: The Structure of Empty Space–Time and Quintessence with Gauge Symmetry Group SU(2) ⊗ U(1)

Round 1

Reviewer 1 Report

Overall Editorial Suggestion: Major revisions

The paper analyzes spin-one bosons on a topological two-dimensional manifold. The descending 

scalar dark-matter/ quintessence particles are evaluated as a Bose-Einstein condensate.

Major revisions

i) Section IIB after Eq. (14) QVF should be completed with reference

Faizal,  Momeni,  Universality of short distance corrections to quantum optics

arXiv:1811.01934.

ii) Section IIB after Eq. (14) 

$\tau, \epsilon$

please comment on the symmetries obtained, and

iia) Section IIB after Eq. (14)

'SDE (12) passes to the Weyl type

equation (1)'

please provide a reference about the mathematical technicalities utilized

iii) After Eq. (44)

please mention a reference book of functions, where the definitions of Legendre functions and normalization choises are explicitely spelled out

iv) Equation after Eq. (93)

please comment on the symmetries obtained

v) At the Planck scale or at the length scales coresponding to the particles studied and at different scales an analysis of Ref.

 suggested in i) could complete the discussion

vi) Conclusions section, last sentence: provide reference to literature for the systems mentioned, and comments, for which the comparison would result otherwise 

unaccomplished

vii) Conclusions section: compare the topological 2D manifold Fig.2 with the symmetries described by Equation after Eq. (93)

with the breaking of a different phase, such as a geometrical phase, a Berry.like phase, Lorentz symmetry, Poincar\'e.particle symmetry, Rarita-Schwinger symmetry, 

other higher-spin particles,

and/or other symmetries and the related manifolds by referring to literature of the choice of the Authors

viia) the Conclucions section could be further completed by adding references of the choice of the Authors and by commenting on them, about possible experimental verifications or confirmations of the model, and/or about what time scales of the Physical hystory of the Universe it can help complete the understanding

Minor revisions

viii) Section I line n1

eliminate the sentence 'and philosophy point of view' 

or complete it with a reference, such as, but not necessarily and/or only, from Philosophical 

Transactions of the Royal Society of London and Philosophy of Physical Science

Edited by Hans Halvorson

Rendering

ix) The one-column formatting should let the text and the equation be of clearer appearence wrt the current formatting

Comments for author File: Comments.txt

Author Response

please find the response file with the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this article the author purpose is to show that massless spin one particles emerges from Yang Mills stochastic equations. Desconsidering if this idea is physically acceptable or not, the major problem with this manuscript is, in my opinion, the use unclear and unconnected statements to "prove" the main results. Definitely, I dont recommend this manuscript for publication in its present form.  

Author Response

please find the response file with the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Report

The paper is very interesting and provides a useful contribution to its area of research. I fully agree with the scientific content and is appropriate for an international journal. The article is readable, the author’s arguments are explained and supported by references. 

Round 2

Reviewer 1 Report

The Authors have performed the reqqeusted tasks.