Alternative Expression for the Electromagnetic Lagrangian

Saldanha, Pablo L.

doi:10.1007/s13538-016-0417-4

Cited by 9 publications

(6 citation statements)

References 20 publications

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“…which would support the conclusion from [32] and what yields the stress-energy tensor for the system in the form of…”

Section: Lagrangian Density For the Systemsupporting

confidence: 83%

Developed method: interactions and their quantum picture

Ogonowski

2023

Front. Phys.

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By developing the previously proposed method of combining continuum mechanics with Einstein’s field equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangian density equal to the invariant of the electromagnetic field was obtained, the vanishing four-divergence of canonical four-momentum appears to be the consequence of the Poynting theorem, and the explicit form of one of the electromagnetic four-potential gauges was introduced. The proposed method allows for further development with additional fields.

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“…which would support the conclusion from [32] and what yields the stress-energy tensor for the system in the form of…”

Section: Lagrangian Density For the Systemsupporting

confidence: 83%

Developed method: interactions and their quantum picture

Ogonowski

2023

Front. Phys.

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“…One of Vaidman's key ideas is that the solenoid is treated as a quantum system that gets reversibly entangled with the charge during the interference, due to the field of the charge on the solenoid being different in different branches. Later, Kang proposed a Lagrangian bearing out Vaidman's model, [8,9] (see also [10]). We shall refer to these as field-based models, as opposed to the standard potential-based model.…”

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confidence: 99%

Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases

Vedral

2020

Phys. Rev. Lett.

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Aharonov and Bohm noted that the wave-function of a charge acquires a detectable phase when superposed along two paths enclosing an infinite solenoid, even though that wave-function is nonzero exclusively where the solenoid's electric and magnetic fields are zero. This phase was long considered radically different from all other quantum phases, because it seems explainable only via local action of gauge-dependent potentials, not of the gauge-invariant electromagnetic fields.Recently Vaidman proposed a model explaining the phase only in terms of the electron's (magnetic) field at the solenoid. Later Kang proposed a Lagrangian model from which Vaidman's can be derived. However, their analysis is still non-local. For it does not explain how the phase, generated at the solenoid, is detectable on the charge when closing the interference loop. To explain this, one needs to quantise the EM field and consider how the interaction between the solenoid and the electron is mediated by photons. In this paper we propose a local model, where the field is quantised. This shows that the Aharonov-Bohm (AB) phase is generated by the same quantum local mechanism as all other electromagnetic phases. Specifically, it is mediated by the entanglement between the superposed charge and the photons. Surprisingly, the quantised model produces some experimentally different predictions from the semiclassical accounts of the AB phase, because it predicts that the phase at any point along the charge path is gauge-invariant and locally generated, and therefore in principle detectable. We propose a realistic experiment, within current technological reach, where the predicted phase difference along the path is measured locally, by performing (a partial) quantum state tomography on the charge without closing the interfering charge paths.

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“…This effect has applications in many areas of physics [2][3][4][5][6][7][8][9][10][11][12][13], but some of its consequences and its implications on the foundations of quantum mechanics are still subjects of active discussion in the literature [14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Magnetic forces in the absence of a classical magnetic field

et al. 2020

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It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced.

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Alternative Expression for the Electromagnetic Lagrangian

Cited by 9 publications

References 20 publications

Developed method: interactions and their quantum picture

Developed method: interactions and their quantum picture

Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases

Magnetic forces in the absence of a classical magnetic field

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