标题： 关于勒夫schetz thumbles的统计：Bell/Leggett-Garg不等式和经典的统计近似 显示英文标题

标题： Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation

摘要： 受Lefschetz纽结理论的启发，我们将量子场论视为具有复概率分布函数（PDF）的统计理论。 这种复值PDF允许违反贝尔型不等式，而实值非负PDF则不能。 本文中，我们在贝尔型不等式的背景下考虑经典-统计近似，即熟悉的（空间）贝尔不等式和时间Leggett-Garg不等式。 我们证明了经典-统计近似不违反时间贝尔型不等式，尽管从某种意义上说它对自由理论是精确的，而全量子理论则可以。 我们解释了这种差异的来源，并指出了空间和时间贝尔型不等式之间的关键区别。 我们还讨论了这项工作对经典-统计近似应用的意义。 显示英文摘要

摘要： 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.