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

## TL;DR

This paper derives the exact form of Maxwell's equations and Dirac's magnetic monopole within Fock's nonlinear relativity, revealing how magnetic charges could exist locally while maintaining overall neutrality.

## Contribution

It provides the first exact formulation of Maxwell's equations and magnetic monopoles in Fock's nonlinear relativity, extending previous approximations.

## Key findings

- Exact form of Maxwell's equations in Fock's nonlinear relativity
- Generalized Dirac magnetic monopole solution
- Magnetic charge can exist locally without violating overall neutrality

## 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.