https://doi.org/10.1140/epjc/s10052-026-15445-1
Regular Article - Theoretical Physics
Bell-CHSH inequality and unitary transformations in quantum field theory
1
Departamento de Física, Universidade Federal de Viçosa (UFV), Avenida Peter Henry Rolfs s/n, 36570-900, Viçosa, MG, Brazil
2
Facultad de Ingeniería, Instituto de Física, Universidad de la República, J. H. y Reissig 565, 11000, Montevideo, Uruguay
3
Departamento de Física Teórica, Instituto de Física, UERJ – Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, 20550-013, Rio de Janeiro, Brazil
4
CBPF – Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
5
Instituto de Física, UFRJ – Universidade Federal do Rio de Janeiro, 21.941-972, Rio de Janeiro, RJ, Brazil
a
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Received:
12
September
2025
Accepted:
15
February
2026
Published online:
6
March
2026
Abstract
Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic quantum field theory. The case of the scalar field in 
Minkowski space-time is scrutinized by relying on the Tomita–Takesaki modular theory. The example of the bounded Hermitian operator 
, where 
stands for the smeared scalar field, is worked out. It is shown that unitary deformations enable for violations of the Bell-CHSH inequality. The setup is generalized to the Proca vector field by means of its equivalence with the scalar theory.
© The Author(s) 2026
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