SciPost Submission Page
The fermionic double smeared null energy condition
by Duarte dos Reis Fragoso, Lihan Guo
Submission summary
| Authors (as registered SciPost users): | Lihan Guo · Duarte dos Reis Fragoso |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00017v1 (pdf) |
| Date submitted: | 2024-11-07 16:58 |
| Submitted by: | dos Reis Fragoso, Duarte |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| 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.
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
Pointwise energy conditions are not respected in quantum field theory, but a variety of quantum energy inequalities have been shown to hold under suitable circumstances. This nicely written paper derives a double-smeared null energy condition DSNEC for Dirac fields in Minkowski space, adapting a method developed by Fewster and Mistry [3] for averages along timelike curves to the double-smeared setting. DSNEC for scalar fields was derived in previous work [1,2].
Apart from a few typos, the derivation appears correct and after some minor corrections I would recommend it for publication.
Requested changes
1- In the abstract both refs [1] & [2] are cited as sources for DSNEC, but in the introduction only [1] is. I think that [2] should also appear here, because this is where DSNEC was actually proved, as far as I understand it.
2- After (5), various symbols, e.g. u's, v's, b's and d's should be defined.
3- After (7), "smear" should be "smearing"
4- In (11) the \alpha subscript is misplaced in the final term
5- In (12) there should be no dagger on the d_\alpha
6- Above (26) I believe that the convolution integral should include a 1/(2\pi) factor and the authors should check the remaining calculation for any consequences.
Also the g's should be \hat{g}'s
7- Similarly (29) lacks factors of \pi and 2\pi
8- After (39) the variable \theta should be explained.
9- After (42) there should be some commentary on why this integral converges, due to the rapid decay of the transforms and the integration range.
10- After (44) sigma_1,2 should be replaced by \sigma_\pm
11- I suggest that the authors also consider the limit of transverse smearing tends to zero, without changing \sigma_+, for consistency check with Section 2
12- In (51) there appears to be a missing factor of 1/2 [cf (35)]. Again, the authors should check for any consequences.
13- In the reference list, the capitalisation of proper names, e.g. Dirac, and acronyms like ANEC, QNEC should be corrected.
14- The authors note that smearing along a null geodesic without transverse smearing results in a trivial bound. They correctly state on p.5 that this is expected, citing the divergence of the bound obtained in [10] as a UV cutoff is removed. An earlier treatment can be found in Phys. Rev. D 67 (2003) 044003, which also gives general reasons for the lack of any QEI over a finite null segment in dimensions higher than 2.
15- A remark: In their conclusion, the authors say that it would be interesting to generalise their results to curved spacetimes. I expect that this is possible, and a starting point might be Class. Quantum Grav. 23 (2006) 6659-6681, which generalises [3] to globally hyperbolic spacetimes.
Recommendation
Ask for minor revision