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BRST invariant formulation of the Bell-CHSH inequality in gauge field theories
by David Dudal, Philipe De Fabritiis, Marcelo Santos Guimaraes, Giovani Peruzzo, Silvio Paolo Sorella
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Submission summary
| Authors (as registered SciPost users): | Philipe De Fabritiis · David Dudal |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2304.01028v1 (pdf) |
| Date submitted: | 2023-04-06 17:29 |
| Submitted by: | De Fabritiis, Philipe |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson's bound. An illustrative comparison with the entangled state of two $1/2$ spin particles in Quantum Mechanics is provided.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023-8-11 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.01028v1, delivered 2023-08-11, doi: 10.21468/SciPost.Report.7641
Strengths
1 - clear and explicit presentation of the construction of BRST-invariant formulations of the Bell-CHSH inequality for two examples of non-interacting Abelian gauge theories
2 - nice interpretation of the presented results by drawing a comparison with a simple quantum mechanical example
Weaknesses
1 - considerable redundancies in the constructions in chapter II, III and V
Report
I recommend the submitted manuscript for publication in SciPost Phys. I is well-written and allows the reader the follow all steps of the explicit computation.
Requested changes
I consider below requested changes to be optional:
The authors might want to consider removing some of the mentioned redundancies which are rooted in the analogous constructions of secs. II, III and IV. This would increase the readability of the manuscript, since in the current version, one might get the feeling that one is reading the same thing over and over again. Due to the explicitness of the computations in secs. III and V, in my opinion the example given in sec. II does not add a lot to the manuscript, and might even be dropped.
Furthermore, I have some additional minor remarks:
- the authors might want to be a bit more careful with distinguishing between three- and four-vectors in eqs. (11)-(14)
- it is unclear to me how the authors arrive at the conclusion directly below eq. (47) from the respective eqs. above. maybe they can elaborate their argument a bit further.
Report #1 by Reinhard Alkofer (Referee 1) on 2023-7-17 (Invited Report)
- Cite as: Reinhard Alkofer, Report on arXiv:2304.01028v1, delivered 2023-07-17, doi: 10.21468/SciPost.Report.7516
Strengths
1- The authors discuss very nicely how the quantum entanglement of squeezed states in quantum gauge field theories can be reformulated to be based on BRST-invariant states. The manuscript is very well written, and all the main arguments can be followed step by step.
Weaknesses
1- The remarks on the entanglement properties of the Minkowski vacuum when expressed by means of the Rindler wedges should either be elaborated more or left out. (This remark does not apply if in the meantime ref. [52] has been published.
Report
As argued above this is a well written manuscript on an important issue in quantum field theory.
I recommend to accept this article for publication.
Requested changes
1- A minor remark (optional change): In the introduction in the paragraph on proposed experimental tests the authors might wish to cite Bertlmann:2001sk, i.e.,
R.~A.~Bertlmann and B.~C.~Hiesmayr,
``Bell inequalities for entangled kaons and their unitary time evolution,''
Phys. Rev. A \textbf{63} (2001), 062112
doi:10.1103/PhysRevA.63.062112
[arXiv:hep-ph/0101356 [hep-ph]].
as a quite early example.