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

Abstract

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.

Maxwell’s equations and Lorentz force in doubly special relativity

“…In the quest for new generalizations even more satisfying, we plan to pursue this work, establish an extended form of the basic laws of gravity and investigate the existence of the magnetic charge in the near future. As a source of inspiration, we can take advantage of our exact studies [29], [30] as well as [26], [27], [48]. Finally, many other analogies and more detailed analysis could also be envisaged as new perspectives, e.g., [24], [42], [49]- [53].…”

“…Unlike Fock's nonlinear relativity where the symmetry between indices µ and ν is kept intact with respect to the deformation induced by the radius of the universe R [28] and [29], we note here that [x µ , ẋν ] (1) does not in general equal [x ν , ẋµ ] (1) . It is also notable that the symmetric corrective part in (55) has a similar form as that found in [28].…”

“…After that, the linear approximation of the κ-deformed geodesic equation is derived and some interpretations are given in [27]. Recently, we have succeeded to go beyond our first-order generalization [28], by establishing the exact formulation of Maxwell's equations, Dirac's magnetic monopole [29] and Lorentz force [30] in the context of Fock-Lorentz transformation [31]- [36]. By restoring the deformed Lorentz algebra, we have predicted that the universe could locally contain the magnetic charge but in its totality it is still neutral [29].…”

“…Recently, we have succeeded to go beyond our first-order generalization [28], by establishing the exact formulation of Maxwell's equations, Dirac's magnetic monopole [29] and Lorentz force [30] in the context of Fock-Lorentz transformation [31]- [36]. By restoring the deformed Lorentz algebra, we have predicted that the universe could locally contain the magnetic charge but in its totality it is still neutral [29]. In [30], the generalized Lorentz force is characterized by a separability between mass and charge where the new effect emerges as the result of coexistence of the radius of the universe, mass and the square of the velocity, but completely independent of electromagnetic field (gravitational-type Lorentz force).…”

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

“…As soon as they appeared in the literature, they have immediately been put to use as tools to investigate deviations from what is predicted for phenomena relying on Heisenberg's uncertainty principle or those phenomena relying on the usual relativistic dispersion relation (see, e.g., Refs. [6][7][8][9][10][11][12] and the review papers [13,14]). In addition, it is well known that these two concepts are actually related to each other.…”