Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory
G. Peruzzo, S. P. Sorella
Abstract
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.
Topics & Concepts
Bell test experimentsPath integral formulationCHSH inequalityPropagatorFeynman diagramQuantum mechanicsMathematical physicsMathematicsPhysicsBell's theoremBell stateQuantumQuantum entanglementQuantum Mechanics and ApplicationsQuantum Electrodynamics and Casimir EffectNoncommutative and Quantum Gravity Theories