Dimensional reduction of electromagnetism

TL;DR

This paper derives simplified one- and two-dimensional models of classical electromagnetism using Hadamard's method, showing how lower-dimensional theories emerge as special cases with uniform fields along extra spatial directions.

Contribution

It introduces a systematic derivation of low-dimensional electromagnetism models from higher dimensions via Hadamard's descent method, clarifying their relationship.

Findings

Two independent electromagnetisms in two spatial dimensions.

Four independent electromagnetisms in one spatial dimension.

Unified framework for low-dimensional electromagnetism models.

Abstract

We derive one- and two-dimensional models for classical electromagnetism by making use of Hadamard's method of descent. Low-dimensional electromagnetism is conceived as a specialization of the higher dimensional one, in which the fields are uniform along the additional spatial directions. This strategy yields two independent electromagnetisms in two spatial coordinates, and four independent electromagnetisms in one spatial coordinate.