Author:
Millington Peter,Mou Zong-Gang,Saffin Paul M.,Tranberg Anders
Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference38 articles.
1. J. S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
2. L. V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
3. J. S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics Physique Fizika 1 (1964) 195 [INSPIRE].
4. A. J. Leggett and A. Garg, Quantum mechanics versus macroscopic realism: is the flux there when nobody looks?, Phys. Rev. Lett. 54 (1985) 857 [INSPIRE].
5. J. Klauder and B. Skagerstam, Coherent states — applications in physics and mathematical physics, World Scientific, Singapore (1985).
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