Stochastic mechanics and the Feynman integral

Pavon, Michele

doi:10.1063/1.1286880

Cited by 14 publications

(9 citation statements)

References 26 publications

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“…However soon after, it was pointed out by Cameron and Daletskii [3,37,38] that a straightforward generalization does not exist, as the complex measure necessary to construct such an equivalence will have an infinite total variation. Later Pavon [39] showed that, if one considers, instead of the process (3.4), a bidirectional Nelson process defined by…”

Section: Stochastic Mechanics and The Feynman-kac Theoremmentioning

confidence: 99%

Analytic Continuation of Stochastic Mechanics

Kuipers

2021

Preprint

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We study a (relativistic) Brownian motion on a complexified (pseudo-)Riemannian manifold. Using Nelson's stochastic quantization, we derive three equivalent descriptions for this problem. If the process has a purely real pseudo-variance, we obtain the ordinary dissipative Brownian motion. In this case, the result coincides with the Feyman-Kac formula. On the other hand, for a purely imaginary pseudo-variance, we obtain a conservative Brownian motion, which provides a description of a quantum particle on a curved spacetime.

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Section: Stochastic Mechanics and The Feynman-kac Theoremmentioning

confidence: 99%

Analytic Continuation of Stochastic Mechanics

Kuipers

2021

Preprint

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“…An extension of the Feynman-Kac theorem to the real time path integral is given by the Feynman-Itô theorem [14,15]. Although this theorem does not have an immediate stochastic interpretation, the real time path integral has been related explicitly to the stochastic quantization framework [16].…”

Section: Introductionmentioning

confidence: 99%

Stochastic quantization of relativistic theories

Kuipers

2021

Journal of Mathematical Physics

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“…Quantum Mechanics (QM), including Quantum Field Theory (QFT), is the most successful mathematical framework of physical theories, with regard to its broad scope of applications and accuracy of predictions; but it is also a battle field of deep metaphysical debates. Besides the orthodox interpretation [1], [2], [3], [4], different alternative schools have appeared [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]; to get a wide view of the present state of the art is a though undertaking (see for example [21], [22], [23], [24], [25], [26], obviously not up to date).…”

Section: Introductionmentioning

confidence: 99%

A Local Interpretation of Quantum Mechanics

López¹

2015

Found Phys

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It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical consequences: the projection rule could be applied in one or the other temporal(?) order of measurements (being non local in any case), but symmetry of the roles of both subsystems would be broken.An alternative theory is presented in which this ambiguity does not exist. Observable relative frequencies differ from those of orthodox Quantum Mechanics, and a gendaken experiment is proposed to falsify one or the other theory. In the alternative theory, each subsystem has an individual state in its own Hilbert space, and the total system state is direct product (rank one) of both, so there is no entanglement. Correlation between subsystems appears through a hidden label that prescribes the output of arbitrary hypothetical measurements.Measurement is treated as a usual reversible interaction, and this postulate allows to determine relative frequencies when the value of a magnitude is known without in any way perturbing the system, by measurement of the correlated companion.It is predicted the existence of an accompanying system, the de Broglie wave, introduced in order to preserve the action reaction principle in indirect measurements, when there is no interaction of detector and particle. Some action on the detector, different from the one cause by a particle, should be observable.

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Stochastic mechanics and the Feynman integral

Abstract: The Feynman integral is given a stochastic interpretation in the framework of Nelson’s stochastic mechanics employing a time-symmetric variant of Nelson’s kinematics recently developed by the author

Cited by 14 publications

References 26 publications

Analytic Continuation of Stochastic Mechanics

Analytic Continuation of Stochastic Mechanics

Stochastic quantization of relativistic theories

A Local Interpretation of Quantum Mechanics

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