On Maxwell's electrodynamics in two spatial dimensions

TL;DR

This paper explores Maxwell's electrodynamics in two spatial dimensions, focusing on retarded potentials and radiation, highlighting fundamental differences from three-dimensional cases and providing insights suitable for advanced undergraduate courses.

Contribution

It presents a detailed construction of Maxwellian electrodynamics in 2+1 dimensions and analyzes the unique features of wave solutions and radiation in this reduced dimensional setting.

Findings

Retarded potentials in 2D differ from 3D cases

Wave solutions in 2D have distinct properties

Radiation behavior in 2D shows unique characteristics

Abstract

We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the usual three-dimensional case arise. These stem from the general form of the solutions of the wave equation in two dimensions, which we discuss using the Green's function method. We believe the topics presented here could be stimulating additions to an advanced electrodynamics course at the undergraduate level.