Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation
Peer reviewed, Journal article
Published version
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https://hdl.handle.net/11250/2835389Utgivelsesdato
2021Metadata
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Originalversjon
Millington, P., Mou, Z-G., Saffin, P.M., Tranberg, A. (2021) Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation. Journal of High Energy Physics (JHEP), 77 (2021) 10.1007/JHEP03(2021)077Sammendrag
Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be violated by a real-valued, non-negative PDF. In this paper, we consider the Classical-Statistical approximation in the context of Bell-type inequalities, viz. the familiar (spatial) Bell inequalities and the temporal Leggett-Garg inequalities. We show that the Classical-Statistical approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory, whereas the full quantum theory does. We explain the origin of this discrepancy, and point out the key difference between the spatial and temporal Bell-type inequalities. We comment on the import of this work for applications of the Classical-Statistical approximation.