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.
Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory
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abstract
The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter.
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On a class of bounded Hermitian operators for the Bell-CHSH inequality in Quantum Field Theory
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.