2013
DOI: 10.1088/1742-6596/442/1/012018
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Amplitudes for spacetime regions and the quantum Zeno effect: pitfalls of standard path integral constructions

Abstract: Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is t… Show more

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Cited by 3 publications
(3 citation statements)
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“…In particular, it has been shown that the current of probability described by the Schrödinger equation can point in the opposite direction of all available momentum components [9,10]. It is therefore reasonable to ask whether quantum theory might require modifications to Newton's first law [11][12][13]. Unfortunately, it is difficult to identify such modifications using only a statistical analysis of the available data.…”
mentioning
confidence: 99%
“…In particular, it has been shown that the current of probability described by the Schrödinger equation can point in the opposite direction of all available momentum components [9,10]. It is therefore reasonable to ask whether quantum theory might require modifications to Newton's first law [11][12][13]. Unfortunately, it is difficult to identify such modifications using only a statistical analysis of the available data.…”
mentioning
confidence: 99%
“…If so, this would increase the relevance of the n-site hopper. The decoherence functional or quantum measure in the continuum is not yet able to be defined for events other than finite unions of events corresponding to finite sequences of projections onto position [5,11,30,31]. If the n-site hoppers have a continuum limit one could potentially use this to define the quantum measure of an event in the continuum as the limit of a sequence of appropriate n-site hopper events as n → ∞.…”
Section: Discussionmentioning
confidence: 99%
“…Quantum mechanics replaces the precise concepts of particle position and particle momentum with the rather less clear concept of a quantum state that describes only the statistical distributions of possible particle positions and particle momenta. Since statistical statements are by their very nature incomplete, there is much room left for speculation regarding the quantum limit of motion for individual point-like particles [1][2][3][4][5][6]. Interestingly, very little of the discussion has focused on the simplification of quantitative criteria for the evaluation of particle propagation, and most of the proposed experimental approaches involve quite a bit of complicated data analysis [7][8][9][10][11][12].…”
Section: Introductionmentioning
confidence: 99%