Peter Millington
Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation
Millington, Peter; Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders
Abstract
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.
Citation
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, 2021(3), Article 77. https://doi.org/10.1007/jhep03%282021%29077
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 22, 2021 |
Online Publication Date | Mar 8, 2021 |
Publication Date | 2021-03 |
Deposit Date | Mar 9, 2021 |
Publicly Available Date | Mar 25, 2021 |
Journal | Journal of High Energy Physics |
Electronic ISSN | 1029-8479 |
Publisher | Springer Verlag |
Peer Reviewed | Peer Reviewed |
Volume | 2021 |
Issue | 3 |
Article Number | 77 |
DOI | https://doi.org/10.1007/jhep03%282021%29077 |
Keywords | Nuclear and High Energy Physics |
Public URL | https://nottingham-repository.worktribe.com/output/5382297 |
Publisher URL | https://link.springer.com/article/10.1007/JHEP03(2021)077 |
Files
Statistics on Lefschetz thimbles
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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