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arXiv · 2212.14407

On the Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in Quantum Field Theory

Giovani Peruzzo·Silvio Paolo Sorella
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Abstract

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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Giovani Peruzzo, Silvio Paolo Sorella. 2022-12-29. On the Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in Quantum Field Theory. https://doi.org/10.1103/physrevd.107.105001

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