Vacuum Currents for a Scalar Field in Models with Compact Dimensions

Round 1

Reviewer 1 Report

Please see the attachment.

Comments for author File: Comments.pdf

Minor editing of the English language is required.

Author Response

Response to Reviewer Report on “Vacuum Currents for a Scalar Field in Models with Compact Dimensions” by A.A. Saharian

I am grateful to Reviewer for the valuable comments. The paper is revised in accordance of them.

1. Subsection 6.4 is added for the fermionic current density.

2. At the end of Conclusion a paragraph is added about magnetic fields generated by vacuum currents.

Reviewer 2 Report

"see attached file"

Comments for author File: Comments.pdf

Author Response

Response to Reviewer Report on “Vacuum Currents for a Scalar Field in Models with Compact Dimensions” by A.A. Saharian

I am grateful to Reviewer for the recommendation to publication.

Reviewer 3 Report

This is an interesting review on activities, performed under an essential participation by the autor over the last two decades or so, on vacuum current components of a charged scalar field \phi coupled to background gravity (minimally or non-minimally) and a background (pure-gauge) U(1) gauge field along compactified (spatial) dimensions within three different  geometries. The technical mastery of this subject is impressively demonstrated when current components are computed analytically from mode-sum representations of an appropriate Green's function of the scalar field by differentiation and a subsequent coincidence limit. I also welcome how the author motivates physically the analysis of vacuum currents within the various background geometries, and how parallels of his present results to persistent currents in mesoscopic rings are pointed out. 

An essential result of the analysis reviewed here is that in the limit L(p)/a\gg 1 dS and AdS geometries enforce a power-law decay in L(p) in contradistinction to the Minkowskian case where exponential decay is observed.  Here a is the curvature radius and L(p) is the radius of the pth compactified dimension. I think that the authors should include a relativating statement about a potential problem of selfconsistency of such a limit. If the extent of a compactified dimension exceeds the curvature radius of the background geometry one would expect that the classical, physical sources enforcing the (quasi)periodicitiy of the quantum field \phi would also induce a change of the background geometry, at least locally. In addition, there should be a gravitational response to the Casimir effect in the opposite limit L(p)/a\ll 1.

Apart from that there are only minor issues that should be fixed by the author before the paper can be published in Symmetry.

1) l. 23: add references that illustrate `symmetry breaking´and `different kinds of instabilities' 

2) in general, there are articles (the or a) missing in various places thoughout the text

3) l. 54: check spelling `toidally', also in l. 88 `toral' 

4) l. 198: introduce line break in equation

5) Eq. (36): prime as a condition to summation must be introduced

6) Fig. 4: selfconsistency of regime L(p)/a>1, add reamrk to caption

7) l. 802: Hofman -> Hofmann

Minor improvements of English required. 

Author Response

Response to Reviewer Report on “Vacuum Currents for a Scalar Field in Models with Compact Dimensions” by A.A. Saharian

I am grateful to Reviewer for the comments. The suggested corrections are introduced. The misprints are corrected. In accordance of the recommendation by Reviewer, the references [1-9] are added. The prime in Eq. (36) is explained in the paragraph after Eq. (31). A clarification in the caption of Fig. 4 is added about the behavior for large values of the length of the extra dimension.