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

We present an investigation of the Clauser-Horne-Shimony-Holt (CHSH) inequality within a relativistic quantum field theory model built up with a pair of free massive scalar fields o phi A; phi B thorn where, as is customary, the indices oA; B thorn 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 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 Becchi-Rouet-Stora-Tyutin (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.

Automated summary

This study investigates the Clauser-Horne-Shimony-Holt (CHSH) inequality within a relativistic quantum field theory model. A set of bounded Hermitian operators is introduced using Weyl operators, and a CHSH-type correlator is constructed and evaluated. Although the violation of the CHSH inequality is small compared to Tsirelson's bound in quantum mechanics, the model can be used to study Bell's inequalities in more physical cases such as the Higgs models.