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Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators

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arxiv 2501.03186 v2 pith:HVAXV3GQ submitted 2025-01-06 quant-ph hep-thmath-phmath.MP

M. S. Guimaraes , I. Roditi , S. P. Sorella , A. F. Vieira This is my paper · ORCID
classification quant-phhep-thmath-phmath.MP
keywords inequalitiesoperatorsbellfieldmerminquantumtheoryvacuum
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abstract

The use of the vacuum projector $|0 \rangle \langle 0| $ and of the unitary Weyl operators enables us to construct a set of Hermitian dichotomic operators in relativistic scalar Quantum Field Theory in Minkowski spacetime. Employing test functions supported in diamond regions, both Bell and Mermin inequalities are studied by means of a numerical setup. In addition to reporting expressive violations of both inequalities, the cluster property is also checked.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On a class of bounded Hermitian operators for the Bell-CHSH inequality in Quantum Field Theory

    quant-ph 2025-05 conditional novelty 6.0 of 10

    Explicit bounded Hermitian operators built from Weyl operators violate the Bell-CHSH inequality in the vacuum of a 1+1 scalar QFT, with a numerical construction matching modular-theory predictions.

  2. A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory

    hep-th 2025-02 conditional novelty 4.0 of 10

    For a free massive scalar field in 1+1 dimensions, the Araki-Uhlmann relative entropy between a coherent state and the vacuum decreases with mass and increases with region size in numerical tests.

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