Differentiable-path integrals in quantum mechanics

Koch, Benjamin; Reyes, Ignacio A.

doi:10.1142/s0219887815501005

Cited by 3 publications

(1 citation statement)

References 45 publications

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“…We know of attempts to reconstruct the Feynman path integral approach in which only well behaved (differentiable) paths were considered. In that case, as done in [21] the high energy, small time-scale behaviour is rather different from the behaviour of normal quantum mechanics. Even with such a construction, the transition between paths can be obtained by means of transformations that may, in the 'worst' (but probably more realistic) case scenario be also depending on arbitrary choices of the experimental setup in each position.…”

Section: Where Is the Curvature?mentioning

confidence: 94%

The hidden quantum origin of gauge connections

Patrascu¹

2023

Phys. Scr.

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A ﬁbre bundle viewpoint of gauge ﬁeld theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of deﬁning the connection on the ﬁbre bundle, leading to an application of the quantum principles to the geometrical and topological deﬁnition of gauge theories. As a result, one could justiﬁably ask oneself if all interactions of the standard model, and perhaps even classical gravity have some quantum component after all. I employ a standard ﬁbre bundle approach to introduce gauge theories, albeit it is known that a quantum bundle exists, simply because the main scope is to show that in the usual way in which we formulate classical gauge theories one can ﬁnd quantum aspects that have been unknown until now. In a sense, I will try to justify the assessment that if we are to allow for gauge ﬁelds and parallel transport, we may have to allow at least some level of quantumness even in our classical gauge theories. The main statement is that propagation of interactions in spacetime is a quantum phenomenon. After writing the ﬁrst draft of this article I noticed ref. [13] where the authors device entanglement of what they call ”classical light”. This experiment supports my theoretical developments with the distinction that I interpret such phenomena also as fundamentally quantum. The distinction comes from the fact that the quantum nature of the experiments is manifested in a diﬀerent way. My view on this is that there is no purely classical reality, no matter what the scale is at which we consider the description.

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Section: Where Is the Curvature?mentioning

confidence: 94%

The hidden quantum origin of gauge connections

Patrascu¹

2023

Phys. Scr.

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Path Integral Formulation of Fractionally Perturbed Lagrangian Oscillators on Fractal

El-Nabulsi¹

2018

J Stat Phys

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Generalization of uncertainty relation for quantum and stochastic systems

Koide

Kodama

2018

Physics Letters A

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The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions. * Electronic address:

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Differentiable-path integrals in quantum mechanics

Cited by 3 publications

References 45 publications

The hidden quantum origin of gauge connections

The hidden quantum origin of gauge connections

Path Integral Formulation of Fractionally Perturbed Lagrangian Oscillators on Fractal

Generalization of uncertainty relation for quantum and stochastic systems

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