SciPost logo

SciPost Submission Page

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

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Philipe De Fabritiis · David Dudal
Submission information
Preprint Link: scipost_202308_00025v1  (pdf)
Date accepted: 2023-10-09
Date submitted: 2023-08-17 19:21
Submitted by: De Fabritiis, Philipe
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Author comments upon resubmission

Dear Editor,

With this attachment, we would like to briefly summarize the modifications we have made to the manuscript entitled ``BRST invariant formulation of the Bell-CHSH inequality in gauge field theories" in order to accommodate the referee's suggestions. For convenience, we highlight the modifications that we have done throughout the manuscript in \textcolor{magenta}{magenta}. We hope that with the present modifications, the paper is ready to be accepted.

The authors

List of changes

Regarding Report 1:

-Following the referee's suggestion, we decided to remove the comments about Rindler wedges (and the references cited in this part), making minor textual changes to suit the new structure, as one can see on pages 2 and 10.
-We included the reference suggested by the referee [41], and other two relevant references [26, 27] in the same paragraph in the introduction.

Regarding Report 2:

-We reformulated the first paragraph of Sec.II to include an explicit sentence stating that the more experienced reader could skip it. Even though this section is not strictly necessary for what follows, we believe it provides a clear and pedagogical illustration of the whole Kugo-Ojima construction, justifying its presence in the paper.
-We included a sentence below Eq.(47) in order to clarify the statement we made there, as suggested by the anonymous referee.
-We changed the 4-vector notation in Eq.(11), following the anonymous referee's suggestion.

Furthermore, we added a reference [64] and a comment about it in the Conclusion.

Published as SciPost Phys. 15, 201 (2023)

Login to report or comment