Bell Inequalities and Unitary Dynamics in Quantum Field Theory: Scalar and Proca Fields

• URL: http://arxiv.org/abs/2412.03840v2
• Date: Mon, 15 Sep 2025 19:21:49 GMT
• Title: Bell Inequalities and Unitary Dynamics in Quantum Field Theory: Scalar and Proca Fields
• Authors: D. O. R. Azevedo, F. M. Guedes, M. S. Guimaraes, I. Roditi, S. P. Sorella, A. F. Vieira,
• Abstract summary: unitary transformations enhance violations of the Bell-CHSH inequality in quantum field theory.<n>We show that unitary deformations significantly increase the Bell-CHSH violation, approaching the Tsirelson bound.<n>We report the first explicit evaluation of such violation in a vector-field vacuum.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine the role of unitary transformations in enhancing violations of the Bell-CHSH inequality in relativistic quantum field theory. In quantum systems, all relevant observables can be expressed via unitary rotations of reference operators. We extend this perspective to a real massive free scalar field and to the Proca vector field in $(1+1)$ Minkowski spacetime. In two dimensions, the Proca theory carries only one degree of freedom and is known to be equivalent to the scalar theory, implying that both yield identical Bell-CHSH violations. After introducing suitable Hermitian operators, we employ Tomita-Takesaki modular theory to construct spacelike separated observables in the vacuum. We demonstrate that unitary deformations significantly increase the Bell-CHSH violation, approaching the Tsirelson bound, and we report the first explicit evaluation of such violation in a vector-field vacuum.

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