Maxwell’s equations in the context of the Fock transformation and the magnetic monopole

Takka, N.; Bouda, A.; Foughali, T.

doi:10.1139/cjp-2016-0717

Cited by 6 publications

(25 citation statements)

References 22 publications

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“…To first approximation in 1/R, expression (28) reproduces the result found in [9]. Up to now, we have not included the electromagnetic field in the calculation.…”

Section: Maxwell's Equationssupporting

confidence: 56%

“…Here of course, F µν is an antisymmetric tensor which can be, in general, a function of coordinates and velocities. However, as in [9], we can check that F µν depends only on position. Indeed, after a long calculation, by using the Jacobi identity involving one coordinate and two velocities where…”

Section: Maxwell's Equationsmentioning

confidence: 99%

“…The same conclusion was found in the k-Minkowski space-time [7] constituting then a common point between the two deformed Minkowski spaces. Using the iterative method that we have developed in [9], we can find F ν (2) after a very long calculation. The same approach may be used to go further in order to find the higher-order terms.…”

Section: Maxwell's Equationsmentioning

confidence: 99%

“…On a quest for new generalizations even more satisfying, we have chosen once more to focus on Maxwell's equations and Dirac's magnetic monopole in the context of Fock's nonlinear relativity. For this purpose, we propose in what follows to go further than the previous work valid only to first order in the deformation parameter [9], by establishing the corresponding exact formulation.…”

Section: Introductionmentioning

confidence: 99%

“…In [7] and [8], the equivalence between the minimal coupling prescription and Feynmans approach has been discussed in the noncommutative space-time and in the relativistic classical mechanics, respectively. Finally, to first order in the deformation parameter, we have proposed in [9] an extended form of Maxwell's equations in the context of the Fock-Lorentz transformation.…”

Section: Introductionmentioning

confidence: 99%

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Exact form of Maxwell’s equations and Dirac’s magnetic monopole in Fock’s nonlinear relativity

Takka

Bouda

2018

Mod. Phys. Lett. A

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After having obtained previously an extended first approximation of Maxwell's equations in Fock's nonlinear relativity, we propose here the corresponding exact form. In order to achieve this goal, we were inspired mainly by the special relativistic version of Feynman's proof from which we constructed a formal approach more adapted to the noncommutative algebra. This reasoning lets us establish the exact form of the generalized first group of Maxwell's equations. To deduce the second one, we have imposed the electric-magnetic duality. As in the k-Minkowski space-time, the generalized Lorentz force depends on the mass of the particle. After having restored the R-Lorentz algebra symmetry, we have used the perturbative treatment to find the exact form of the generalized Dirac's magnetic monopole in our context. As consequence, the Universe could locally contain the magnetic charge but in its totality it is still neutral.

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“…To first approximation in 1/R, expression (28) reproduces the result found in [9]. Up to now, we have not included the electromagnetic field in the calculation.…”

Section: Maxwell's Equationssupporting

confidence: 56%

Section: Maxwell's Equationsmentioning

confidence: 99%

Section: Maxwell's Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact form of Maxwell’s equations and Dirac’s magnetic monopole in Fock’s nonlinear relativity

Takka

Bouda

2018

Mod. Phys. Lett. A

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The One-dimensional Box Problem and the Dirac Oscillator in R-Minkowski Spacetime

Asli,

Foughali

2024

Int J Theor Phys

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Maxwell’s equations and Lorentz force in doubly special relativity

Takka

Bouda

2019

Indian J Phys

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On the basis of all commutation relations of the κ-deformed phase space incorporating the κ-Minkowski space-time, we have derived in this paper an extended first approximation of both Maxwell's equations and Lorentz force in doubly (or deformed) special relativity (DSR). For this purpose, we have used our approach of the special relativistic version of Feynman's proof by which we have established the explicit formulations of electric and magnetic fields. As in Fock's nonlinear relativity (FNLR), the laws of electrodynamics depend on the particle mass which therefore constitutes a common point between the two extended forms of special relativity. As one consequence, the corresponding equation of motion contains two different types of contributions. In addition to the usual type, another one emerges as a consequence of the coexistence of mass and charge which are coupled with the κ-deformation and electromagnetic field. This new effect completely induced by the κ-deformed phase space is interpreted as the gravitational-type Lorentz force. Unlike FNLR, the corrective terms all depend on the electromagnetic field in DSR.

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Maxwell’s equations in the context of the Fock transformation and the magnetic monopole

Cited by 6 publications

References 22 publications

Exact form of Maxwell’s equations and Dirac’s magnetic monopole in Fock’s nonlinear relativity

Exact form of Maxwell’s equations and Dirac’s magnetic monopole in Fock’s nonlinear relativity

The One-dimensional Box Problem and the Dirac Oscillator in R-Minkowski Spacetime

Maxwell’s equations and Lorentz force in doubly special relativity

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