Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory

Abstract

We present an investigation of the $CHSH$ inequality within a relativistic quantum field theory model built up with a pair of free massive scalar fields $({\phi }_A,{\phi }_B)$ where, as it is customary, the indices $(A,B)$ refer to Alice and Bob, respectively. A set of bounded Hermitian operators is introduced by making use of the Weyl operators. A $CHSH$ type correlator is constructed and evaluated in the Fock vacuum by means of the canonical quantization. Although the observed violation of the $CHSH$ inequality turns out to be rather small as compared to Tsirelson's bound of Quantum Mechanics, the model can be employed for the study of Bell's inequalities in the more physical case of gauge theories such as: the Higgs models, for which local $BRST$ invariant operators describing both the massive gauge boson as well as the Higgs particle have been devised. These operators can be naturally exponentiated, leading to $BRST$ invariant type of Weyl operators useful to analyze Bell's inequalities within an invariant $BRST$ environment.

22 pages, 4 figures

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• Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization
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Cited by in corpus (7)

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• Weyl operators, Tomita-Takesaki theory, and Bell-Clauser-Horne-Shimony-Holt inequality violations
• On the Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in Quantum Field Theory
• Mermin's inequalities in Quantum Field Theory
• BRST invariant formulation of the Bell-CHSH inequality in gauge field theories
• Comments on the Bell-Clauser-Horne-Shimony-Holt inequality
• Using Weyl operators to study Mermin's inequalities in Quantum Field Theory