Exact form of Maxwell's equations and Dirac's magnetic monopole in Fock's nonlinear relativity
arXiv:1902.09440 · doi:10.1142/S0217732318501730
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.
arXiv comment18 pages, 0 figures
References in corpus (15)
- Lorentz invariance with an invariant energy scale
- Testable scenario for Relativity with minimum-length
- Generalized Lorentz invariance with an invariant energy scale
- A time varying speed of light as a solution to cosmological puzzles
- Doubly Special Relativity
- Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
- Relativistic Generalization and Extension to the Non-Abelian Gauge Theory of Feynman's Proof of the Maxwell Equations
- Electrodynamics on -Minkowski space-time
- Maxwell's equations on the -Minkowski spacetime and Electric-Magnetic duality
- Minimal coupling and Feynman's proof
- Dirac monopole with Feynman brackets
- On the Fock Transformation in Nonlinear Relativity
- Maxwell's equations in the context of the Fock transformation and the magnetic monopole
- From Fock's Transformation to de Sitter Space
- Dirac's Equation in -Minkowski Spacetime