Dirac’s Equation in R-Minkowski Spacetime

Foughali, T.; Bouda, A.

doi:10.1007/s10773-015-2863-0

Cited by 7 publications

(5 citation statements)

References 20 publications

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“…This result established a correspondence between the R-Minkowski spacetime and de Sitter's spacetime. Also this correspondence was confirmed since Dirac's equation was derived in R-Minkowski spacetime [9] and it turned out to be exactly the Dirac equation in the conformally de Sitter spacetime. Elsewhere, Dyson [10] claimed that Feynman derived Maxwell's equations and the Lorentz force from Newton's law of motion and the commutator between position and velocity.…”

Section: Introductionmentioning

confidence: 60%

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: 60%

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

2017

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“…From a practical point of view, the relevance of our studies is the proposition of new theoretical challenges to check the validity of the invariance of the speed of light, the homogeneity of space and the uniformity of time in the cosmological context [24]. In an equivalent way, the theoretical results highlighted in FNLR, [15], [16], [25], [26] provide a new series of occasions to test one of the most fundamental concepts of physics, namely, the conservation of the energy at the scale of the universe [24]. To examine the scientific soundness of our predictions, it is obvious that the empirical or observational studies must be focused on the physical phenomena of the large scale in space and/or time.…”

Section: Discussionmentioning

confidence: 81%

“…The main novelty of such rewriting is that the contraction x µ p µ becomes an invariant which made possible the coherent description of free particles in this context. Focusing on the generalizations of both Klein-Gordon and Dirac equations in [25] and [26] respectively, the correspondence between R-Minkowski and de Sitter spacetime has been highlighted.…”

Section: Introductionmentioning

confidence: 99%

Exact form of the generalized Lorentz force in Fock’s nonlinear relativity

Takka

2019

Int. J. Mod. Phys. A

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This work completes a series of two papers devoted to the extension of the fundamental laws of electrodynamics in the context of Fock’s nonlinear relativity (FNLR). Indeed, after having established in the previous study the exact generalizations of both Maxwell’s equations and Dirac’s magnetic monopole, we present here the remaining exact Lorentz force. As in [Formula: see text]-Minkowski space–time, two different contributions appear in the corresponding equation of motion where the new effect is interpreted as the gravitational-type Lorentz force. This common point separately induced by the radius of the universe in our case, or Planck energy in other works, reinforces once more the analogy between electromagnetism and gravity in two different scientific approaches. As a relative difference, it is very important to highlight that more homogeneity characterizes our results where each effect is exclusively generated by mass or charge but not both at the same time. Even more, the new effect emerges as the result of the triple effect of the R-deformation, mass and the square of the velocity but completely independent of electromagnetic field.

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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%

“…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%

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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Dirac’s Equation in R-Minkowski Spacetime

Cited by 7 publications

References 20 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 the generalized Lorentz force in Fock’s nonlinear relativity

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

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