Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory

• URL: http://arxiv.org/abs/2603.25873v1
• Date: Thu, 26 Mar 2026 19:59:52 GMT
• Title: Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory
• Abstract summary: We argue that violations of the Bell-CHSH inequality might occur for different choices of Bell's operators.<n>We also outline a possible path towards the saturation of Tsirelson's bound.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Tomita-Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions. By using the Bisognano-Wichmann results, the construction of a set of wedge localized vectors in the one-particle Hilbert space of a relativistic massive scalar field in $1+1$ dimensions is devised to establish whether violations of the Bell-CHSH inequality might occur for different choices of Bell's operators. In particular, the construction of the wedge localized vectors employed in the seminal work by Summers-Werner is scrutinized and applied to Weyl and other operators. We also outline a possible path towards the saturation of Tsirelson's bound.

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