Aspects of Magnetic Field Configurations in Planar Nonlinear Electrodynamics

TL;DR

This paper investigates how space-time dimensionality affects magnetostatic fields in three-dimensional Born-Infeld Electrodynamics, revealing that such fields are absent without topological terms but appear with Chern-Simons addition.

Contribution

It demonstrates the impact of dimensionality and topological terms on magnetostatic field existence in nonlinear electrodynamics models.

Findings

Magnetostatic fields do not exist for electric charges at rest in 3D Born-Infeld Electrodynamics.

Adding a Chern-Simons term induces magnetostatic fields in the model.

Analysis of fields related to magnetic monopoles in three dimensions.

Abstract

In the framework of three-dimensional Born-Infeld Electrodynamics, we pursue an investigation of the consequences of the space-time dimensionality on the existence of magnetostatic fields generated by electric charges at rest in an inertial frame, which are present in its four-dimensional version. Our analysis reveals interesting features of the model. In fact, a magnetostatic field associated with an electric charge at rest does not appear in this case. Interestingly, the addition of the topological term (Chern-Simons) to Born-Infeld Electrodynamics yields the appearance of the magnetostatic field. We also contemplate the fields associated to the would-be-magnetic monopole in three dimensions.