Feynman path integral formulation of the Bell-Clauser-Horne-Shimony- Holt inequality in quantum field theory

By employing a free scalar quantum field theory model previously introduced [G. Peruzzo and S. P. Sorella, Phys. Rev. D 106, 125020 (2022)], we attempt to formulate the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality within the Feynman path integral. This possibility relies on the observation that the Bell-CHSH inequality exhibits a natural extension to quantum field theory in such a way that it is compatible with the time ordering T. By treating the Feynman propagator as a distribution and by introducing a suitable localizing set of compact support smooth test functions, we work out the path integral setup for the Bell-CHSH inequality, recovering the same results of the canonical quantization.

Automated summary

By employing a free scalar quantum field theory model introduced previously, the authors attempt to formulate the Bell-CHSH inequality within the Feynman path integral. They observe that the Bell-CHSH inequality naturally extends to quantum field theory and is compatible with the time ordering T. By treating the Feynman propagator as a distribution and introducing a suitable set of test functions, they work out the path integral setup for the Bell-CHSH inequality, obtaining the same results as canonical quantization.