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The fermionic double smeared null energy condition
by Duarte dos Reis Fragoso, Lihan Guo
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Lihan Guo · Duarte dos Reis Fragoso |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00017v2 (pdf) |
| Date submitted: | May 21, 2025, 11:11 p.m. |
| Submitted by: | dos Reis Fragoso, Duarte |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Energy conditions are crucial for understanding why exotic phenomena such as traversable wormholes and closed timelike curves remain elusive. In this paper, we prove the Double Smeared Null Energy Condition (DSNEC) for the fermionic free theory in 4-dimensional flat Minkowski space-time, extending previous work on the same energy condition for the bosonic case [1] [2] by adapting Fewster and Mistry’s method [3] to the energy- momentum tensor T_{++}. A notable difference from previous works lies in the presence of the γ_0γ_+ matrix in T_{++}, causing a loss of symmetry. This challenge is addressed by mak- ing use of its square-root matrix. We provide explicit analytic results for the massless case as well as numerical insights for the mass-dependence of the bound in the case of Gaussian smearing.
Author comments upon resubmission
My co-author and I were pleased to receive your response and feedback inviting us to revise and resubmit our manuscript. Accordingly, we would like to submit the enclosed revised paper, for reconsideration for publication as we have revised our manuscript according to the reviewers’ comments.
We would like to thank you for providing your constructive and detailed review comments on our manuscript. The recommendations and advice have helped us to enhance the quality of the manuscript.
All authors have read and approved the revised manuscript. We hope that our resubmission is now suitable for inclusion in SciPost and we look forward to hearing from you.
Thank you for your time,
Best regards,
Duarte Fragoso
List of changes
For medium revisions,
We added some remarks regarding the divergence of single smeared bound both in section 2 and in the conclusion.
We added a comparison to the results in reference [2] in both the massless and massive cases.
We elaborated on the claim regarding the outlook of generalizing the fermionic DSNEC to interacting theory.
To clarify the context,
After (5), various symbols, e.g. u's, v's, b's and d's are be defined.
After (43) the variable \theta is explained.
After (46) we comment on why this integral converges
We add a consistency check after equation (49)
We wrote the proof for double smearing case more explicitly
We also correct several typos pointed out by the reviewers.
The missing dagger in equation (8), (9), (10), (12) and (25) on the d_{\alpha’}
The \alpha appearing as a superscript In equation (13) on v^\alpha.
In equation (14) there should not be a \dagger on the the d^\dagger_\alpha.
In the sentence above equation (24) it’s “a lower bound” rather than “an upper bound”
In the last paragraph in section 3.2 we mean the averaged null energy condition (ANEC) instead of NEC
Complete Footnote 3.
After (9), we change “smear" into “smearing"
The missing 1/(2\pi) factor in the convolution integral and the pre-factor involved
After (48) sigma_1,2 is replaced by \sigma_\pm
The capitalisation of proper names in the reference list.
Moreover, we thanked the reviewers in the aknowlegments.
Current status:
Reports on this Submission
Strengths
1- This is the first work to consider the DSNEC for non-scalar fields. 2- Generally clear presentation.
Weaknesses
1- Some typos and possible missing factors.
Report
a) In Appendix A, as noted in my first report, the expression for $ \gamma_+$ in (A.6) is missing a factor of 1/2, arising from lowering the index from $\gamma^+ =\gamma^0+\gamma^1$ using the metric (A.1). Compare with the factor of 1/2 in $k_+$. This should be corrected and has potential consequences throughout the manuscript, as it feeds in to the matrix A and the stress-energy tensor component $T_{++}$.
b) On p.7, l.127, "applying lemma 1 again" is incorrect - it is (29) that is used here.
c) l.152-153 - it's not quite correct to say that all terms vanish, because that is not true of the last one. The discussion of convergence could be simplified by estimating each term in the $v$-integral separately. The $v$-integral for terms with a power $v^a$ for $a\ge 0$ can be estimated less than $\int_0^\infty dv\, v^a |\hat{g}(v)|^2$ multiplied by terms depending on $u$, while those with $a<0$ can be estimated less than $(m^2/u)^a \int_0^\infty dv |\hat{g}(v)|^2$, again multiplied by terms depending on $u$. The $v$-integrals now converge as do the remaining u ones.
Regarding the journal - it seems to me that this is not ground-breaking in the sense required for SciPost Physics but it is in principle publishable in SciPost PhysicsCore.
Requested changes
1- Fix the factor in $\gamma_+$ and any consequences throughout the manuscript 2- Fix wording as in comment (b) 3- Consider improving the wording as in (c).
Recommendation
Ask for minor revision