On the Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in Quantum Field Theory
Abstract
By employing a free scalar Quantum Field Theory model previously introduced Peruzzo:2022pwv, we attempt at formulating the 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.
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