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Quantum Foundations

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

arXiv
Authors: J. G. A. Caribé, M. S. Guimaraes, I. Roditi, S. P. Sorella

Year

2026

Paper ID

39116

Status

Preprint

Abstract Read

~2 min

Abstract Words

96

Citations

N/A

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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  • This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • The Tomita-Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.25873 [2] arXiv https://arxiv.org/abs/2603.25873 [3] Publisher https://arxiv.org/abs/2603.25873

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