From Fock's Transformation to de Sitter Space

Foughali, T.; Bouda, A.

doi:10.48550/arxiv.1605.01943

Cited by 3 publications

(6 citation statements)

References 4 publications

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“…The corresponding first Casimir is constructed and allowed the derivation of the Klein-Gordon equation which turned out to be the Klein-Gordon equation in de Sitter Space given by its conformal metric [8]. This result established a correspondence between the R-Minkowski spacetime and de Sitter's spacetime.…”

Section: Introductionmentioning

confidence: 93%

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

2017

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In the R-Minkowski space-time, which we recently defined from an appropriate deformed Poisson brackets that reproduce the Fock coordinate transformation, we derive an extended form for Maxwell's equations by using a generalized version of Feynman's approach. Also, we establish in this context the Lorentz force. As in deformed special relativity, modifying the angular momentum in such a way as to restore the R-Lorentz algebra generates the magnetic Dirac monopole.

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Section: Introductionmentioning

confidence: 93%

“…constituting the phase space algebra of the R-Minkowski spacetime [8]. Here η µν = (+1, −1, −1, −1) and µ, ν = 0, 1, 2, 3.…”

Section: Introductionmentioning

confidence: 99%

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

2017

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“…From [18] and [19], the quantization of the R-deformed phase space algebra gives us the following result…”

Section: Maxwell's Equationsmentioning

confidence: 99%

“…In this section, we will examine the hypothesis of the existence of Dirac's magnetic monopole by studying the impact that induces the R-deformation of the three commutators [x µ , x ν ], [x µ , ẋν ] and [ ẋµ , ẋν ] on the R-Lorentz algebra satisfying the following relations [18] x µ ,…”

Section: The R-lorentz Algebra Symmetrymentioning

confidence: 99%

“…The main novelty of this rewriting is that the contraction x µ p µ becomes an invariant which made possible the coherent description of free particles by means of plane waves. In [18] and [19], the correspondence between the R-Minkowski spacetime and de Sitter spacetime has been established after having derived the Klein-Gordon and Dirac equations, respectively. 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.…”

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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Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method

Hammad,

Landry,

Dijamco

2021

Preprint

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We examine the influence of the dispersion relation on the Unruh effect by Lorentz boosting the phase of Minkowski vacuum fluctuations endowed with an arbitrary dispersion relation. We find that, unlike what happens with a linear dispersion relation exhibited by massless fields, thermality is lost for general dispersion relations. We show that thermality emerges with a varying "apparent" Davies-Unruh temperature depending on the acceleration of the observer and on the degree of departure from linearity of the dispersion relation. The approach has the advantage of being intuitive and able to pinpoint why such a loss of thermality occurs and when such a deviation from thermality becomes significant. We discuss the link of our results with the well-known fundamental difference between the thermalization theorem and the concept of Rindler noise. We examine the possible experimental validation of our results based on a successful setup for testing the classical analogue of the Unruh effect recently described in the literature.

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From Fock's Transformation to de Sitter Space

Cited by 3 publications

References 4 publications

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

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

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

Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method

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