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

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