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By employing a free scalar Quantum Field Theory model previously introduced
\cite{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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