Extended symmetrical classical electrodynamics

TL;DR

This paper proposes a modified classical electrodynamics framework without point charges, introducing induced charges and currents dependent on a vector k, and explores its implications for monopole fields and boundary conditions.

Contribution

It develops a new modified electrodynamics theory with a unique Lagrangian, defines conditions for a single potential, and analyzes monopole solutions with discrete spectrum of the parameter k.

Findings

Modified equations include induced charges and currents.

Static solutions describe fields inside electric monopoles.

Boundary conditions imply a discrete spectrum for the parameter k.

Abstract

In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector k and the vectors of the electromagnetic field E and B. It is shown that the vectors E and B can be defined in terms of two 4-potentials and the components of k are the components of the 4-tensor of the third rank. The Lagrangian of modified electrodynamics is defined. The conditions are derived at which only one 4-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of the electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector k has a discrete spectrum. The electric and magnetic fields, energy and angular momentum of the monopole are found for different eigenvalues of k.