Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality

• URL: http://arxiv.org/abs/2605.06224v1
• Date: Thu, 07 May 2026 13:19:17 GMT
• Title: Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality
• Abstract summary: Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in Quantum Field Theory.<n>We give an explicit rapidity-space realization of the Summers-Werner modular-localization construction.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner modular-localization construction and reduce the vacuum Bell-CHSH correlator to a single spectral weight $h^2(ω)$ for the modular operator. The resulting analytic families approach the Tsirelson bound in the vacuum state as their spectral weight concentrates near $ω\approx0$, corresponding to the eigenvalue $λ^2 \approx 1$ of the modular operator.

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