论文标题
Lefschetz Thimbles的统计数据：Bell/Leggett-Garg不平等和经典统计近似
Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation
论文作者
论文摘要
受Lefschetz Thimble理论的启发，我们将量子场理论视为具有复杂概率分布函数（PDF）的统计理论。这种复杂值的PDF允许违反贝尔型不平等，而实现的，非负的PDF不能违反。在本文中，我们考虑了贝尔型不平等现象的经典统计近似，即。熟悉的（空间）铃铛不平等和暂时的leggett-garg不平等。我们表明，即使在某种意义上说，这对于自由理论来说是确切的，而完整的量子理论确实确实如此。我们解释了这种差异的起源，并指出了空间和时间钟形不平等之间的关键区别。我们评论这项工作的导入到经典统计近似的应用中。
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.
